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THE  DECENNIAL  PUBLICATIONS  OF 
THE  UNIVERSITY  OF  CHICAGO 


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EDITED   BY    A   COMMITTEE   APPOINTED   BY   THE   SENATE 

EDWAED  CAPPS 
STARE  WILLAED  CUTTING  EOLLIN  D.  SALISBURY 

JAMES  EOWLAND  ANGELL      WILLIAM  I.  THOMAS  SHAILEE  MATHEWS 

GAEL  DAELING  BUCK  FEEDEEIC  IVES  CAEPENTEE         OSKAE  BOLZA 

JULIUS  STIEGLITZ  JACQUES  LOEB 


260014 


THESE  VOLUMES  ARE  DEDICATED 

TO    THE   MEN   AND   WOMEN 

OP    OUR   TIME    AND   COUNTRY   WHO    BY   WISE   AND   GENEROUS   GIVING 

HAVE   ENCOURAGED   THE   SEARCH    AFTER   TRUTH 

IN    ALL   DEPARTMENTS    OP    KNOWLEDGE 


LIGHT  WAYES   ANT)    THEIR    USES 


LIGHT  WAVES  AND  THEIR 

USES 


BY 

A.  A.  MICHELSON 

OF  THE  DEPAETMENT  OF  PHYSICS 


THE  DECENNIAL  PUBLICATIONS 
SECOND  SERIES     VOLUME  III 


CHICAGO 

THE  UNIVERSITY  OF  CHICAGO  PRESS 

1903 


Copyright  1002 

BY  THE   UNIVERSITY  OF  CHICAGO 


PREFACE 

This  series  of  eight  lectures  on  "Light  Waves  and  Their 
Uses"  was  delivered  in  the  spring  of  1899  at  the  Lowell 
Institute.  In  the  preparation  of  the  experiments  and  the 
lantern  projections  I  was  ably  assisted  by  Mr.  C.  R.  Mann, 
to  whom  I  am  further  indebted  for  editing  this  volume. 

I  have  endeavored,  possibly  at  the  risk  of  inelegance  of 
diction,  to  present  the  lectures  as  nearly  as  possible  in  the 
words  in  which  they  were  originally  given,  trusting  that 
thereby  some  of  the  interest  of  the  spoken  addresses  might 
be  retained. 

While  it  is  hoped  that  the  work  will  be  intelligible  to  the 
general  reader,  it  is  also  possible  that  some  of  the  ideas  may 
be  of  interest  to  physicists  and  astronomers  who  may  not 
have  had  occasion  to  read  the  somewhat  scattered  published 
papers. 

A.    A.    MiCHELSON. 
Ryeeson  Physical  Laboratory 
The  University  of  Chicago 
October,  1902 


CONTENTS 

Lecture         I.     Wave  Motion  and  Interference      -        -        -        1 

Lectube  II.  Comparison  of  the  Efficiency  of  the  Micro- 
scope Telescope,  and  Interferometer  -        -       19 

Lecture  III.  Application  of  Interference  Methods  to  Meas- 
urements of  Distances  and  Angles     -        -      44 

Lecture  IV.  Application  of  Interference  Methods  to  Spec- 
troscopy     -------      60 

Lecture        V.    Light  Waves  as  Standards  of  Length  -         -       84 

Lecture  VI.  Analysis  of  the  Action  of  Magnetism  on 
Light  Waves  by  the  Interferometer  and 
the  Echelon        ------     107 

Lecture    VII.     Application    of    Interference     Methods    to 

Astronomy  ------     128 

Lecture  VIII.     The  Ether      -         -        -        -        -        -         -    147 

Index        -----------     165 


LECTURE  I 

WAVE    MOTION  AND    INTERFERENCE 

Science,  when  it  has  to  communicate  the  results  of  its 
labor,  is  under  the  disadvantage  that  its  language  is  but 
little  understood.  Hence  it  is  that  circumlocution  is  inevi- 
table and  repetitions  are  difficult  to  avoid.  Scientific  men 
are  necessarily  educated  to  economize  expression  so  as  to 
condense  whole  sentences  into  a  single  word  and  a  whole 
chapter  into  a  single  sentence.  These  words  and  sentences 
come  to  be  so  familiar  to  the  investigator  as  expressions  of 
summarized  work  —  it  may  be  of  years  —  that  only  by  con- 
siderable effort  can  he  remember  that  to  others  his  ideas 
need  constant  explanation  and  elucidation  which  lead  to 
inartistic  and  wearying  repetition.  To  few  is  it  given  to 
combine  the  talent  of  investigation  with  the  happy  faculty 
of  making  the  subject  of  their  work  interesting  to  others.  I 
do  not  claim  to  be  one  of  these  fortunate  few;  and  if  I  am 
not  as  successful  as  I  could  wish  in  this  respect,  I  can  only 
beg  your  indulgence  for  myself,  but  not  for  the  subject  I 
have  chosen.  This,  to  my  mind,  is  one  of  the  most  fasci- 
nating, not  only  of  the  departments  of  science,  but  of  human 
knowledge.  If  a  poet  could  at  the  same  time  be  a  physicist, 
he  might  convey  to  others  the  pleasure,  the  satisfaction, 
almost  the  reverence,  which  the  subject  inspires.  The 
aesthetic  side  of  the  subject  is,  I  confess,  by  no  means  the 
least  attractive  to  me.  Especially  is  its  fascination  felt  in 
the  branch  which  deals  with  light,  and  I  hope  the  day  may 
be  near  when  a  Ruskin  will  be  found  equal  to  the  descrip- 
tion of  the  beauties  of  coloring,  the  exquisite  gradations  of 
light  and  shade,  and  the  intricate  wonders  of   symmetrical 

1 


2  Light  Waves  and  Their  Uses 

forms  and  combinations  of  forms  which  are  encountered  at 
every  turn. 

Indeed,  so  strongly  do  these  color  phenomena  appeal  to 
me  that  I  venture  to  predict  that  in  the  not  very  distant 
future  there  may  be  a  color  art  analogous  to  the  art  of 
sound  —  a  color  music,  in  which  the  performer,  seated  be- 
fore a  literally  chromatic  scale,  can  play  the  colors  of  the 
spectrum  in  any  succession  or  combination,  flashing  on  a 
screen  all  possible  gradations  of  color,  simultaneously  or  in 
any  desired  succession,  producing  at  will  the  most  delicate 
and  subtle  modulations  of  light  and  color,  or  the  most 
gorgeous  and  startling  contrasts  and  color  chords !  It  seems 
to  me  that  we  have  here  at  least  as  great  a  possibility  of 
rendering  all  the  fancies,  moods,  and  emotions  of  the  human 
mind  as  in  the  older  art. 

These  beauties  of  form  and  color,  so  constantly  recurring 
in  the  varied  phenomena  of  refraction,  diffraction,  and  inter- 
ference, are,  however,  only  incidentals ;  and,  though  a  never- 
failing  source  of  aesthetic  delight,  must  be  resolutely  ignored 
if  we  would  perceive  the  still  higher  beauties  which  appeal 
to  the  mind,  not  directly  through  the  senses,  but  through 
the  reasoning  faculty;  for  what  can  surpass  in  beauty  the 
wonderful  adaptation  of  Nature's  means  to  her  ends,  and  the 
never-failing  rule  of  law  and  order  which  governs  even  the 
most  apparently  irregular  and  complicated  of  her  manifes- 
tations? These  laws  it  is  the  object  of  the  scientific 
investigator  to  discover  and  apply.  In  such  successful 
investigation  consists  at  once  his  keenest  delight  as  well  as 
his  highest  reward. 

It  is  my  purpose  to  bring  before  you  in  the  following 
lectures  an  outline  of  a  number  of  investigations  which  are 
based  on  the  use  of  light  waves.  I  trust  I  may  be  pardoned 
for  citing,  as  illustrations  of  these  uses,  examples  which  are 
taken  almost  entirely  from  my  own  work.      I  do  this  because 


Wave  Motion  and  Inteefeeence  3 

I  believe  that  I  shall  be  much  more  likely  to  interest  you  by 
telling  what  I  know,  than  by  repeating  what  someone  else 
knows. 

In  order  to  discuss  intelligently  these  applications  of 
light  waves,  it  will  be  necessary  to  recall  some  fundamental 
facts  about  light  and  especially  about  wave  motion.  These 
facts,  though  doubtless  familiar  to  most  of  us  here,  need  em- 
phasis and  illustration  in  order  that  we  may  avoid,  as  far  as 
possible,  the  tedious  repetition  against  which  we  were  warned. 

Doubtless  there  are  but  few  who  have  not  watched  with 
interest  the  circular  waves  produced  by  a  stone  cast  into  a 
still  pond  of  water,  the  ever- widening  circles,  going  farther 
and  farther  from  the  center  of  disturbance,  until  they  are 
lost  in  the  distance  or  break  on  the  shore.  Even  if  we  had 
no  knowledge  of  the  original  disturbance,  its  character,  in  a 
general  way,  might  be  correctly  inferred  from  the  waves. 
For  instance,  the  direction  and  distance  of  the  source  can  be 
determined  with  considerable  accuracy  by  drawing  two  lines 
perpendicular  to  the  front  of  the  wave ;  the  source  would  lie 
at  their  intersection.  The  size  of  the  waves  will  give  infor- 
mation concerning  the  size  of  the  object  thrown.  If  the  waves 
continue  to  beat  regularly  on  the  shore,  the  disturbance  is 
continuous  and  regular  ;  and,  if  regular,  the  frequency  (i.  e., 
the  number  of  waves  per  second)  determines  whether  the 
disturbance  is  due  to  the  splash  of  oars,  to  the  paddles  of  a 
steamer,  or  to  the  wings  of  an  insect  struggling  to  escape. 

In  a  precisely  similar  manner,  though  usually  without 
conscious  reasoning  about  the  matter  on  our  part,  the  sound 
waves  which  reach  the  ear  give  information  regarding  the 
source  of  the  sound.  Such  information  may  be  classified  as 
follows : 

1.  Direction  (not  precise). 

2.  Magnitude  (loudness). 


Light  Waves  and  Their  Uses 


3.  Frequency  (pitch). 

4.  Form  (cliaracter). 

Light  gives  precisely  the  same  kinds  o£  information,  and 
hence  it  is  only  natural  to  infer  that  light  also  is  a  wave  motion. 
We  know,  in  fact,  that  it  is  so  ;  but  before  giving  the  evi- 
dence to  prove  it,  it  will  be  well  to  make  a  little  preliminary 
study  of  the  chief  characteristics  of  wave  motion. 


.   ; H i  1 1 ! } I! ! i I r i n i ! • . ( t n f ; ■ 


FIG.  1 

One  of  the  difficulties  encountered  in  studying  wave 
motion  is  the  rapidity  of  the  propagation  of  the  waves.  A 
fairly  moderate  speed  is  attained  by  the  waves  propagated 
along  a  spiral  spring.  If  one  end  of  such  a  spring  be 
fastened  to  a  wooden  box  on  the  wall  of  the  lecture-room, 
while  the  other  end  is  held  in  the  hand,  we  can  see  that  any 
motion  communicated  by  the  hand  is  successively  trans- 
mitted to  the  different  parts  of  the  spring  until  it  reaches 
the  wall.  Here  it  is  reflected  back  toward  the  hand,  but 
with  diminished  amplitude.  We  can  also  see  that  any  kind 
of  transverse  motion,  /.  c,  motion  at  right  angles  to  the 
length  of  the  spring,  whether  regular  or  irregular,  gives 
rise  to  a  corresponding  wave  form  wliich  travels  along  the 
spring  with  a  velocity  that  is  th(^  same  in  every  case. 

If  the   S[)riiig  be   very  suddenly  stretched  or  relaxed,  a 


Wave  Motion  and  Interference  5 

wave  of  longitudinal  vibrations  passes  along  it,  announcing 
its  arrival  at  the  other  end.  by  a  sound  at  the  box ;  the  time 
occupied  in  the  passage  being  perceptibly  less  than  that 
required  for  the  transverse  wave.' 

The  velocity  of  the  wave  is  in  both  cases  too  great  to  ad- 
mit of  convenient  investigation.  In  order  to  familiarize  the 
student  with  wave 
motion,  a  number 
of  mechanical  de- 
vices have  been 
constructed,  such 
as  that    shown  in 


< 


2 


Fig.  1.     Such  me-  fig. 

chanical  models  imitate  wave  motions  rather  than  produce 
them.  They  are  purely  kinematic  illustrations,  and  not 
true  wave  motions;  for  in  the  latter  the  propagation  is  de- 
termined by  the  forces  and  inertias  which  exist  within  the 
system  of  particles  through  which  the  wave  is  moving. 

The  wave  model  of  Lord  Kelvin  is  free  from  this  objec- 
tion. It  consists  of  a  vertical  steel  wire  on  which  blocks 
of  wood  are  fastened  at  regular  intervals.  It  is  very  essen- 
tial that  these  blocks  should  not  slip  on  the  wire,  and  this 
end  is  best  accomplished  by  bending  the  wire,  in  the  middle 
of  each  block,  around  three  small  nails,  as  shown  in  Fig.  2. 
For  the  sake  of  symmetry  two  such  pieces  may  be  fastened 
together,  with  the  wire  passing  between  them.  Attention 
may  be  fixed  upon  the  motion  of  the  ends  of  the  blocks,  by 
driving  into  them  large,  gilt,  upholstering  tacks — a  device 
which  adds  considerably  to  the  attractiveness  of  the  experi- 
ment.    The  complete  apparatus  is  shown  in  Fig.  3. 

On  giving  the  lowest  element  a  twist,  the  torsion  pro- 
duced in  the  wire  will  communicate  the  twist  to  the  next 
element,  etc.     The  twist  thus  travels  along  the  entire  row, 

1 1  am  indebted  to  Professor  Cross  for  this  illustration. 


Light  Waves  and  Theik  Uses 


< —       » 

r  =» 

r  > 

r  > 

■  —  I 

<  =3 

i  -  3 

t  _  1 

< « 

' ^ »■ 


moving  more  slowly  the  smaller  the  wire  and 
the  heavier  the  blocks,  so  that,  by  varying 
these  two  factors,  any  desired  speed  may  be 
obtained. 

The  wave  form  which  is  propagated  in  any 
of  the  various  possible  cases  is,  in  general, 
very  complicated.  It  can  be  shown,  however, 
that  it  is  always  possible  to  express  such  forms, 
however  complex,  by  a  series  of  simple  sine 
curves  such  as  that  represented  in  Fig.  4. 
The  study  of  wave  motion  may  be  much  sim- 
plified by  this  device.  Accordingly,  in  all  that 
follows,  except  where  the  contrary  is  expressly 
stated,  it  will  be  assumed  that  we  are  dealing 
with  waves  of  this  simple  type. 

There  are  certain  characteristics  of  wave 
motion  of  which  we  shall  have  to  speak  fre- 
quently in  what  follows,  and  which  therefore 
need  definition.  In  the  first  place,  the  shape 
of  the  wave  illustrated  in  Fig.  4  is  important. 
It  is  the  curve  which  would  be  drawn  by  a 
pendulum,  carrying  a  marker,  upon  a  piece  of 
smoked  glass  moving  uniformly^at  right  angles 
to  the  motion  of  the?  pendulum.  Since  the 
pendulum  moves  in  what  is  called  simple  har- 
monic motion,  the  curve  is  called  a  simple  har- 
monic curve,  or  a  sine  curve.  The  amplitude 
of  the  wave  is  the  maximum  distance  of  a  crest 
or  a  trough  from  the  position  of  rest,  i.  e.,  from 
the  straight  line  drawn  through  the  middle  of 
the  curve.  The  period  of  the  vibration  is  the 
time  it  takes  one  particle  to  execute  one  com- 
plete vibration ;  /.  e. ,  to  revert  to  the  pendulum, 
•=y^  it  is  the  time  it  takes  the  pendulum  to  execute 

FIG.  3 


r » 

<  :  » 

'  —  — » 

■  —  ■ 

■  —  — » 
«                -  « 

«  ■  t 

I =:         » 

1 1 


en: 
« 

I 
■ 

« 

ez: 


czir 


Wave  Motion  and  Interfeeence  7 

one  complete  swing. ^  The  phase  of  any  particle  along  the 
curve  is  the  portion  of  a  complete  vibration  which  the  par- 
ticle has  executed.  The  ivave  length  is  the  distance  between 
two  particles  in   the  same  phase.     Thus  it  is  the  distance 


FIG.  4 

between  two  consecutive  crests  or  between  two  consecutive 
troughs.  When  all  the  particles  vibrate  in  one  plane,  e.  g., 
the  plane  of  the  drawing,  the  wave  is  said  to  be  polarized  in 
a  plane.  The  velocity  of  propagation  of  the  wave  is  the  dis- 
tance traveled  by  any  given  crest  in  one  second. 

As  has  just  been  stated,  the  type  of  wave  motion  illus- 
strated  in  Fig.  4  may  be  approximately  realized  by  impart- 
ing the  motion  of  a  pendulum  or  a  tuning-fork  to  one  end 
of  a  very  long  cord.  It  can  be  shown  that  after  a  time 
every   particle  of  the  cord   will  vibrate  with  precisely  the 


FIG.  5 

same  motion  as  that  of  the  pendulum  or  tuning-fork  from 
which  the  disturbance  starts.  Any  particular  phase  of  the 
motion  occurs  a  little  later  in  every  succeeding  particle ;  and 
it  is  this  transmission  of  a  given  phase  along  the  cord 
which  constitutes  the  wave  motion. 

1  In  some  works  the  half  of  this  is  taken,  /.  e.,  the  time  it  takes  a  pendulum  to 
move  from  the  extreme  left  to  the  extreme  right. 


8  Light  Waves  and  Their  Uses 

Very  elementary  considerations  show  that  the  length  {I) 
of  the  wave  is  connected  with  the  period  (p)  of  vibration  of 
the  particles  (the  time  of  one  complete  cycle)  and  the 
velocity  {v)   of  transmission  by  the   simple  relation  I  —  pv. 


FIG.  6 

In  fact,  if  we  could  take  instantaneous  photographs  of  such 
a  train  of  waves  at  equal  intervals  of  time,  say  one-eighth 
of  the  period,  they  would  appear  as  in  Fig.  5.  It  will  readily 
be  seen  that  in  the  eight-eighths  of  a  period  the  wave  has 
advanced  through  just  one  wave  length,  while  any  particle 
has  gone  once  through  all  its  phases. 

Let  us  next  consider  the  superposition  of  two  similar  trains 
of  waves  of  equal  period  and  amplitude.  If  the  phases  of  the 
two  wave  trains  coincide,  the  resulting  wave  train  will  have 
twice  the  amplitude  of  the  components,  as  shown  in  Fig.  6. 
If,  on  the  other  hand,  the  phase  of  one  train  is  half  a  period 
ahead  of  that  of  the  other,  as  in  Fig.  7,  the  resulting  ampli- 


FIG.  7 

tude  is  zero;  that  is,  the  two  motions  exactly  neutralize 
each  other.  In  the  case  of  sound  waves,  the  first  case  cor- 
responds to  fourfold  intensity,  the  second  to  absolute  silence. 
The  principle  of  which  these  two  cases  are  illustrations  is 
miscalled  interference;  in  reality  the  result  is  that  each  wave 
motion  occurs  exactly  as  if  the  other  were  not  there  to  inter- 


Wave  Motion  and  Inteeference 


9 


fere.     The  name  has,  however,  the  sanction  of  long  usage,  and 
will  therefore  be  retained.     The  principle  of  interference  is  of 


FIG.  8 


such  fundamental  importance  that  it  will  be  worth  while  to 

impress  it  upon  the  mind  by  a  few  experimental  illustrations. 

Fig.   8   represents    an    apparatus    devised   by    Professor 

Quincke  for  illustrating  interference  of  sound.     An  organ 


10 


Light  Waves  and  Theie  Uses 


pipe  is  sounded  near  the  base  of  the  instrument.  Thence 
the  sound  waves  are  conducted  through  the  two  vertical 
tubes,  one  of  which  is  capable  of  being  lengthened,  like  a 
trombone.      They  then    reunite    and    are    conducted    by   a 


FIG.  9 


single  tube  to  a  "  manometric  capsule,"  which  impresses  the 
resulting  vibrations  on  a  gas  jet,  the  trembling  of  the  jet 
being  rendered  visible  in  a  revolving  mirror. 

When  the  two  branch  tubes   are  of  equal  length,  the 
waves   reach  the    flame   in  the   same   phase,   causing   it   to 


FIG.  10 

vibrate,  as  shown  by  the  character  of  the  image  in  the 
revolving  mirror.  Fig.  9;  while,  if  one  of  the  branches  be 
made  half  a  wave^  longer  than  the  other,  the  disturbance 
disappears,  and  the  image  appears  as  shown  in  Fig.  10. 

A  very  simple  and  instructive  experiment  may  be  made 

1  The  length  required  will  depend  on  the  tone  of  the  orniin  pipe.    For  middle  C 
(2.'j6  vibrations  per  second)  the  double  length  rcciuired  is  two  feet. 


Wave  Motion  and  Interference 


11 


by  throwing  simultaneously  two  stones  into  still  water,  and 
a  number  of  interesting  variations  may  be  obtained  by 
varying  the  size  of  the  stones  and  their  distance  apart. 

The  experiment  may  be  arranged  for  projection  by  using 
a  surface  of  mercury  instead  of  one  of  water,  and  agitating 
it  by  means  of  a  tuning- 
fork,  to  the  ends  of  whose 
prongs  are  attached  light 
pieces  of  iron  wire  which 
dip  slightly  into  the  mer- 
cury. 

The  arrangement  of 
the  apparatus  is  shown  in 
Fig,  11.  The  light  of  an 
electric  lamp  is  concen- 
trated on  a  small  mirror, 
by  which  it  is  reflected 
through  a  lens  to  the 
tuning-fork,  whose  ends 
dip  into  a  surface  of  mer- 
cury. It  is  reflected  by 
the  mercury  surface  back  through  the  lens  and  passes  to 
another  mirror,  by  which  it  is  reflected  to  form  an  image 
on  a  distant  screen.  Fig.  12  shows  the  resulting  disturbance 
of  the  surface.  The  circular  ripples  which  diverge  from  the 
points  of  contact  of  the  forks  are  represented  by  the  circles. 
These  move  too  rapidly  to  be  seen  in  the  actual  experiment, 
but  may  be  readily  recognized  in  an  instantaneous  photo- 
graph. The  heavy  lines  are  the  lines  of  maximum  disturb- 
ance, where  the  two  systems  of  waves  meet,  always  in  the 
same  phase ;  while  the  lighter  parts  between  represent  the 
quiescent  portions  of  the  surface,  where  the  crests  of  one 
system  meet  the  troughs  of  the  other,  forming  stationary 
waves.     Fig.  13  is  a  photograph  of  the  actual  appearance. 


FIG.  11 


12  Light  Waves  and  Theie  Uses 

Another  striking  instance  of  interference  is  furnished  by 
two  tuning-forks  of  nearly  the  same  pitch.  Take,  first,  two 
similar  forks  mounted  on  resonators.  When  these  are  sounded 
by  a  cello  bow,  the  resultant  tone  may  or  may  not  be  louder 
than  the  component  tones, but  it  is  constant — or,  at  least,  dies 
away  very  slowly.     If,  now,  one  of  the  forks  be  loaded  by 


FIG.  12 

fastening  a  small  weight  to  the  prong,  the  sound  sinks  and 
swells  at  regular  intervals,  producing  the  well-known  phenom- 
enon of  "beats."  The  maximum  occurs  when  the  two  vibra- 
tions are  in  the  same  phase.  Gradually  the  loaded  fork  loses 
on  the  other  until  it  is  half  a  vibration  behind ;  then  there  is 
a  brief  silence.  This  may  be  shown  graphically  by  allowing 
each  fork  to  trace  its  own  record  along  a  piece  of  smoked 
glass,  and  by  adding  the  two  sine  curves,  as  shown  in  Fig.  14. 

The  matter  of  the  interference  of  light  waves  requires 
special  treatment  on  account  of  the  enormous  rapidity  of 
the  vibrations.  This  statement,  however,  inverts  the  actual 
chronology,  for  this  rapidity  is  inferred  from  the  interference 
experiments  themselves. 


Wave  Motion  and  Inteeference 


13 


A  beautiful   instance   of    such  interference  occurs   in  a 
soap  film.     Ordinarily,  however,  such  films  have  the  form 


FIG.  13 


of  a  soap  bubble;  and,  while  the  disturbing  causes  usually 
in  operation  enhance  wonderfully  the  beauty  of  the  appear- 
ance, they  do  not  permit  the  accurate  investigation  of  the 

VVXAAAAAAAAAAAAAAAAAAAAAAAAAAAAA/ 
AAAAAAAAAAAAAAAAAAAAAAAAAAAA 

FIG.  14 

phenomenon.  These  disturbing  elements  are  very  much 
diminished  in  the  arrangement  which  follows: 


1-t 


Light  Waves  and  Theik  Uses 


A  soap  solution  is  made  up  as  follows :  One  part  of  fresh 
Castile  soap  is  dissolved  in  forty  parts  of  warm  water ;  when 
cool,  three  parts  of  the   solution  are  mixed  with  two  parts 

of  glycerine.  The 
mixture  is  cooled 
to  a  temperature 
of  3°  or  4^0.,  and 
filtered.  A  soap 
film  is  formed  by 
dipping  into  the 
solution  a  short 
piece  of  wide  glass 
tubing.  Remov- 
ing the  tube  and 
placing  it  so  that 
the  film  is  vertical, 
a  series  of  beauti- 
fully colored  bands 
appear,  the  colors 
being  deeper  at  the 
top  and  gradually 
fading  into  barely  perceptible  alternations  of  pink  and  green 
near  the  bottom.  The  bands  broaden  out  as  the  film  gets 
thinner,  but  the  succession  of  colors  remains  the  same  and 
may  be  described  as  follows:  The  top  of  the  film  is  black; 
then  the  colors  in  the  first  band  are  bluish  gray,  white,  yellow, 
and  red ;  those  in  the  second  band  are,  in  order,  violet,  blue, 
green,  yellow,  red;  the  third  band  is  blue,  green,  yellow,  and 
red;  and  the  succeeding  bands  green  and  red.  The  colors 
are  best  observed  by  using  the  film  as  a  mirror  to  reflect  the 
light  from  a  white  wall;  or  the  light  from  a  lantern  may  be 
reflected  to  a  lens  which  forms  an  image  of  the  film  on  a 
screen. 

The  colors  of  thin  films  and  of  interference  phenomena 


FIG.  15 


Wave  Motion  and  Interference  15 

generally  are  among  the  most  beautiful  in  nature,  and  while 
no  artist  could  do  justice  to  such  a  subject,  much  less  a 
lithographic  plate,  such  a  plate  (Plate  II)  may  be  used  to 
recall  the  more  striking  characteristics. 

For  the  scientific  investigation  of  the  interference  of  light 
waves,  however,  the  soap  film  is  rather  unsatisfac- 
tory on  account  of  the  excessive  mobility  of  its  parts 
and  the  resulting  changes  in  thickness.  A  much  more 
satisfactory  arrangement  for  this  purpose  is  the  fol- 
lowing: Two  pieces  of  glass  with  optically  plane 
surfaces  are  carefully  cleaned  and  freed  from  dust 
particles.  A  single  fiber  of  silk  is  placed  on  one  of 
the  surfaces  near  the  edge,  and  the  other  is  pressed 
against  it,  thus  forming  an  extremely  thin  wedge 
of  air  between  the  two  plates,  as  shown  in  Fig.  16.     ^^^'  ^^ 

It  will  be  found  that  in  this  case  the  succession  of  colored 
bands  will  resemble  in  every  respect  those  in  the  soap  film, 
except  that  they  are  now  permanent.  The  light  is  reflected 
from  all  four  surfaces,  and  hence  the  purity  of  the  colors  is 
somewhat  dimmed  by  the  first  and  the  fourth  reflections. 
These  may  be  obviated  by  using  wedges  of  glass  instead  of 
plates. 

To  account  for  the  colored  fringes  it  will  be  best  to  begin 
with  the  simpler  case  of  monochromatic  light.  If  a  piece  of 
red  glass  is  interposed  anywhere  in  the  path  of  the  light, 
the  bands  are  no  longer  colored,  but  are  alternately  red  and 
black.  They  are  rather  more  numerous  than  before,  and  a 
trifle  wider.  If  a  blue  glass  is  interposed,  the  bands  con- 
sist of  alternations  of  blue  and  black,  and  are  somewhat 
narrower  (cf.  Plate  II). 

Let  us  suppose  now  that  red  light  consists  of  waves  of 
very  small  length.  The  train  of  waves  reflected  by  the  first 
surface  of  the  film  will  be  in  advance  of  that  reflected  by  the 
second  surface.     At  the  point  where  the  two  surfaces  touch 


16  Light  Waves  and  Theie  Uses 

each  other  the  advance  is,  of  course,  zero;  and  here  we 
should  have  the  two  wave  trains  in  the  same  phase,  with  a 
consequent  maximum  of  light.  Where  the  thickness  of  the 
film  is  such  that  the  second  wave  train  is  half  a  wave  behind, 
there  should  be  a  dark  band ;  at  one  whole  wave  retardation, 
a  bright  band;  and  so  on. 

The  alternations  of  light  and  dark  bands  are  thus 
accounted  for,  but  the  experiment  shows  that  the  first  band 
is  dark  instead  of  bright.  This  discrepancy  is  due  to  the 
assumption  that  both  reflections  took  place  under  like  condi- 
tions, and  that  the  phase  of  the  two  trains  of  waves  would  be 
equally  affected  by  the  act  of  reflection.  This  assumption 
is  wrong,  for  the  first  reflection  takes  place  from  the  inner 
surface  of  the  first  glass,  while  the  second  occurs  at  the  outer 
surface  of  the  second  glass.  The  first  reflection  is  from  a 
rarer  medium — the  air;  while  the  second  is  from  a  denser 
medium  —  the  glass.  A  simple  experiment  with  the  Kelvin 
wave  apparatus  will  illustrate  the  difference  between  the  two 
kinds  of  reflection.  The  upper  end  of  this  apparatus  is  fixed, 
while  the  lower  end  is  free ;  the  fixed  end,  therefore,  represents 
the  surface  of  a  denser  medium,  the  free  end  that  of  a  rarer 
medium.  If  now  a  wave  be  started  at  the  lower  end  by 
twisting  the  lowest  element  to  the  right,  the  twist  travels 
upward  till  it  reaches  the  ceiling,  whence  it  returns  with  a 
twist  to  the  left — i.  e.,  in  the  opposite  phase.  When,  how- 
ever, this  left  twist  reaches  the  lowest  element,  it  is  reflected 
and  returns  as  a  twist  to  the  left  —  so  that  the  reflection  is 
in  the  same  phase. 

There  is  thus  a  difference  of  phase  of  one-half  a  period 
between  the  two  reflections,  and,  when  this  is  taken  into 
account,  experiment  and  theory  fully  agree.  We  may  now 
make  use  of  the  experiment  to  find  a  rough  approximation 
to  the  length  of  the  light  waves. 

If  we  measure  by  the  microscope  the  diameter  of  the  fila- 


Wave  Motion  and  Interfekenoe 


17 


ment  which  separates  the  glasses,  it  will  be  found  to  be, 
say,  two  and  seven-tenths  microns/  Counting  the  number 
of  dark  bands  in  red  light,  we  find  there  are  eight;  and 
hence  we  conclude  that  at  the  thickest  part  of  the  air  film 
the  retardation  is  eight  waves,  and  hence  the  distance  sepa- 
rating the  glasses  —  that  is,  the  thickness  of  the  filament — 
is  four  waves,  which  gives  about  sixty-eight  hundredths  of 

V 
B 

G 
Y 
O 
R 

FIG.  17 

a  micron  for  the  wave  length  of  red  light.  If  blue  light  is 
used,  there  will  be  twelve  dark  bands,  whence/  the  wave 
length  of  blue  light  is  forty-five  hundredths  of  a  micron. 

The  following  table  gives  the  approximate  wave  lengths 
of  the  principal  colors: 

Red      -        -        -        -    0.68  microns 
Orange     -        -        -  .63 


Yellow 
Green 
Blue 
Violet 


.58 
.53 
.48 
.43 


Fig.  17  gives  a  diagram  of  the  wave  lengths  of  the  dif- 
ferent colors,  magnified  about  twenty  thousand  times. 

SUMMAEY 

Waves  give  information  concerning  direction,  distance, 
magnitude,  and  character  of  the  source.  Light  does  the 
same ;  hence  the  presumption  in  favor  of  the  hypothesis  that 
light  consists  of  waves. 

1  A  micron  is  a  thousandth  of  a  millimeter,  or  about  a  twenty-five  thousandth  of 
an  inch. 


18  Light  Waves  and  Theie  Uses 

Wave  trains  may  destroy  each  other  by  "interference." 
Light  added  to  light  may  produce  darkness. 

The  reason  why  interference  is  not  more  frequently 
apparent  in  the  case  of  light  is  that  light  waves  are  exceed- 
ingly minute. 

By  the  measurement  of  interference  fringes  it  is  possible 
to  measure  the  length  of  light  waves,  and  the  results  of  such 
measurements  show  that  the  wave  lengths  are  different  for 
different  colors. 


LECTURE  II 

COMPARISON  OP  THE  MICROSCOPE  AND  TELESCOPE 
WITH  THE  INTERFEROMETER 

One  of  the  principal  objections  which  have  been  urged 
against  the  wave  theory  of  light  is  the  fact  that  light  appears 
to  travel  in  straight  lines,  whereas  sound,  which  is  known 
to  be  a  wave  motion,  does  not  cast  a  shadow;  in  other 
words,  the  sound  waves  are  capable  of  bending  around  an 
obstacle  in  the  path  of  the  waves. 

We  shall  now  not  only  try  to  show  that  both  of  these  two 
statements  are  untrue,  or,  at  least,  only  approximately  true, 
but  we  shall  actually  show  that  sound  waves  do  cast  a  shadow 
and  that  light  waves  do  not  move  in  straight  lines.  The 
effect,  in  fact,  depends  on  the  length  of  the  wave,  and  we 
may  say  roughly  that  the  reason  why  a  sound  shadow  is 
not  ordinarily  observed  is  that  the  obstacles  themselves  are 
of  the  same  order  of  magnitude  as  the  length  of  the  sound 
waves.  If,  therefore,  we  wish  to  cast  a  sound  shadow,  it 
will  be  necessary  to  use  either  very  large  screens  or  very 
short  waves  —  that  is,  high  sounds.  Indeed,  the  effect  will 
be  most  evident  if  we  use  sounds  that  are  barely  within  the 
limits  of  audition,  or  in  some  cases  higher  than  can  be  per- 
ceived by  the  ear;  and  it  will  be  interesting  to  trace  the 
relation  between  the  definiteness  of  the  sound  shadow  and 
the  shortness  of  the  sound  wave. 

I  have  here  a  whistle  whose  length  is  about  one  inch.  It 
produces,  therefore,  a  sound  wave  of  the  length  of  four 
inches.  In  order  to  show  to  an  audience  the  effect  of  the 
whistle  at  different  points  on  the  other  side  of  an  obstacle,  it 
is  convenient  to  use  what  is  termed  a  "sensitive  flame." 

19 


20  Light  Waves  and  Theie  Uses 

This  flame  is  produced  by  allowing  a  jet  of  gas  to  issue 
under  considerable  pressure  from  a  small  nozzle,  and  by 
gradually  increasing  the  pressure  until  the  flame  is  on  the 
point  of  flaring.  On  blowing  the  whistle,  we  observe  that 
the  flame  ducks;  it  is  lowered  to  perhaps  one-third  or  one- 
fourth  of  its  height,  and  broadens  out  at  the  same  time. 
On  placing  the  whistle  behind  an  obstacle,  we  observe  by 
the  ducking  of  the  flame  that  it  responds  to  the  whistle 
almost  as  readily  as  when  no  obstacle  was  present. 

I  now  take  a  shorter  whistle,  half  an  inch  long;  which, 
therefore,  produces  a  sound  wave  two  inches  long.  The 
flame  responds  even  more  readily  to  this  than  to  the  longer 
whistle,  and  when  the  shorter  whistle  is  sounded  behind 
the  obstacle  the  flame  ducks,  but  to  a  much  less  marked 
degree  than  before. 

I  have  here  the  means  of  producing  still  higher  sounds. 
Strung  on  a  piece  of  wire  are  a  number  of  iron  washers  — 
rings  of  iron  about  an  inch  in  diameter.  When  these  are 
shaken  they  produce  vibrations  whose  wave  length  is  even 
shorter  than  that  produced  by  the  whistle  just  sounded.  On 
shaking  the  rings  you  perceive  the  immediate  response  of 
the  flame,  and  on  shaking  the  rings  behind  the  obstacle  the 
flame  responds  still,  but  much  more  feebly.  I  take  a  new 
set  of  rings  one-half  inch  in  diameter.  On  shaking  these 
the  flame  responds  as  before,  but  when  I  place  the  rings 
behind  the  obstacle  the  flame  scarcely  responds  at  all.  I 
take  a  still  smaller  series  of  discs.  These  are  approximately 
only  one-fourth  of  an  inch  in  diameter  and  produce  a  wave 
whose  length  is  approximately  one-half  inch.  On  shaking 
the  last  set  of  discs  outside  the  obstacle  the  flame  responds 
not  quite  so  strongly  as  before,  because  the  total  amount  of 
energy  in  this  case  is  very  small;  but,  on  shaking  the  discs 
behind  the  obstacle,  the  flame  is  absolutely  quiescent,  show- 
ing that  the  sound  shadow  is  perfect.     In  moving  the  discs 


MicEoscoPE,  Telescope,  Interferometer     21 

to  and  fro  while  shaking  them,  the  geometrical  limit  of  the 
shadow  can  be  definitely  marked  to  within  something  like  half 
an  inch;  that  is,  a  quantity  of  the  same  order  as  the  length 
of  the  sound  wave  which  is  being  used. 

It  is  evident  from  the  foregoing  that,  if  we  wish  to  inves- 
tigate the  bending  of  light  waves  around  a  shadow,  we  must 
take  into  account  the  fact  which  has  already  been  established, 
namely,  that  the  light  waves  themselves  are  exceedingly 
small  —  something  of  the  order  of  a  fifty-thousandth  of  an 
inch.  The  corresponding  bending  around  an  obstacle  might, 
therefore,  be  expected  to  be  a  quantity  of  this  same  order; 
hence,  in  order  to  observe  this  effect,  special  means  would 
have  to  be  adopted  for  magnifying  it. 

The  diffraction  of  sound  waves  is  beautifully  shown  by 
the  following  experiment : '  A  bird  call  is  sounded  about  ten 
feet  from  a  sensitive  flame,  and  a  circular  disc  of  glass  about 
a  foot  in  diameter  is  interposed.  If  the  adjustment  is  imper- 
fect, the  sound  waves  are  completely  cut  off;  but  when  the 
centering  of  the  plate  is  exact,  the  sound  waves  are  just  as 
efiicient  as  though  the  obstacle^  were  removed. 

This  surprising  result  was  first  indicated  by  Poisson, 
and  was  considered  a  very  serious  objection  to  the  undula- 
tory  theory  of  light.  It  was  naturally  considered  absurd  to 
say  that  in  the  very  center  of  a  geometrical  shadow  there 
should  not  only  be  light,  but  that  the  brightness  should  be  fully 
as  great  as  though  no  obstacle  were  present.  The  experi- 
ment was  actually  tried,  however,  and  abundantly  confirmed 
the  remarkable  prediction. 

The  experiment  cannot  be  shown  to  an  audience  by  pro- 
jecting on  a  screen,  but  an  individual  need  have  no  difficulty 
in  observing  the  effect.  The  image  of  an  arc  light  (or,  better, 
of  the  sun)  is  concentrated  on  a  pinhole  in  a  card,  and  the 
light  passing  through  is  observed  by  a  lens  of  two  or  three 

1  Exhibited  by  Lord  Rayleigh  at  the  Royal  Institute. 


22  Light  Waves  and  Theik  Uses 

inclies'  focal  length  some  twenty  feet  distant.  About  half- 
way a  disc  of  about  a  quarter-inch  diameter,  and  very 
smoothly  and  accurately  turned,  is  suspended  by  three 
threads,'  so  that  its  center  is.  accurately  in  line  with  the  pin- 
hole and  the  center  of  the  lens.  The  field  of  the  lens  will 
now  be  quite  dark,  except  at  the  center  of  the  shadow,  where 
a  bright  point  of  light  is  seen. 

We  shall  now  attempt  to  show  the  analogue  of  the  sound- 
shadow  experiment  by  means  of  light  waves.     The  light  is 


FIG.  18 

concentrated  on  a  very  narrow  slit  A  (Fig.  18),  which  may 
be  supposed  to  act  as  the  source  of  light  waves.  Another 
slit  B,  about  an  inch  wide,  is  placed  at  a  distance  of  about 
eight  feet,  and  beyond  this '  a  screen  C  receives  the  light 
which  has  passed  through  B.  The  borders  bh  of  the  shadow 
of  the  slit  B  are  quite  sharply  defined  (though  a  very  slight 
bending  of  the  light  around  the  edges  may  be  observed  by 
means  of  a  lens  focused  on  h).  But  if  the  slit  be  made 
narrow,  as  at  B' ,  the  sharp  boundary  which  should  appear 
at  cc  is  diffuse  and  colored,  the  light  being  bent  into  the 
geometrical  shadow  as  indicated  by  the  dotted  lines.  The 
narrower  the  second  slit  is  made,  the  wider  and  more  diffuse 
will  be  the  image  on  the  screen;  that  is  to  say,  the  greater 
will  be  the  amount  of  bending  into  the  shadow.  An  inter- 
esting variation  of  the  experiment  is  made  by  using  two  slits 
instead  of  the  second  slit  B.     In  this  case,  in  addition  to  the 

1  Tho  disc  may  be  glued  to  a  piece  of  optical  glass,  care  being  taken  that  no 
trace  of  glue  appears  beyond  the  edge  of  the  disc. 


MiGEOSCOPE,  Telescope,  Inteeferometee     23 

bending  of  the  rays  from  their  geometrical  path,  we  have 
the  interference  of  the  light  from  the  two  slits,  producing 
interference  bands  whose  distance  apart  is  greater  the  closer 
the  two  slits  are  together.  If  instead  of  two  slits  we  have  a 
very  large  number,  such  as  would  be  produced  by  a  number 
of  very  fine  parallel  wires,  we  have,  in  addition  to  the  cen- 
tral, sharp  image,  two  lateral,  colored  images,  which,  when 
carefully  examined,  show  in  their  proper  order  all  the 
colors  of  the  spectrum.  This  arrangement  is  known  as  a 
diffraction  grating,  and,  though  mentioned  here  simply 
as  an  instance  of  diffraction  or  bending  of  the  rays  from 
their  geometrical  path,  will  be  shown  in  a  subsequent  lec- 
ture to  have  a  very  important  application  in  spectrum 
analysis. 

We  have  thus  shown  that  light  consists  of  waves  of 
exceeding  minuteness,  and  have  found  approximate  values  of 
the  lengths  of  the  waves  by  measuring  the  very  small  inter- 
val between  the  surfaces  at  the  thicker  end  of  our  air  wedge. 
It  can  be  shown  also  that  this  same  measurement  may  be 
accomplished  with  a  grating  if  we  know  the  small  interval 
between  its  lines.  The  question  naturally  arises:  Might 
it  not  be  advantageous  to  reverse  the  process,  and,  utilizing 
this  extreme  minuteness  of  light  waves,  make  our  measure- 
ments of  length  or  angle  with  a  correspondingly  high  order 
of  accuracy?  The  principal  object  of  these  lectures  is  to 
illustrate  the  various  means  which  have  been  devised  for 
accomplishing  this  result. 

Before  entering  into  these  details,  however,  it  may  be  well 
to  reply  to  the  very  natural  question:  What  would  be  the 
use  of  such  extreme  refinement  in  the  science  of  measure- 
ment ?  Very  briefly  and  in  general  terms  the  answer  would 
be  that  in  this  direction  the  greater  part  of  all  future  dis- 
covery must  lie.  The  more  important  fundamental  laws  and 
facts  of  physical  science  have  all  been  discovered,  and  these 


24  Light  Waves  and  Their  Uses 

are  now  so  firmly  established  that  the  possibility  of  their  ever 
being  supplanted  in  consequence  of  new  discoveries  is  exceed- 
ingly remote.  Nevertheless,  it  has  been  found  that  there 
are  apparent  exceptions  to  most  of  these  laws,  and  this  is 
particularly  true  when  the  observations  are  pushed  to  a  limit, 
i.  e.,  whenever  the  circumstances  of  experiment  are  such  that 
extreme  cases  can  be  examined.  Such  examination  almost 
surely  leads,  not  to  the  overthrow  of  the  law,  but  to  the  dis- 
covery of  other  facts  and  laws  whose  action  produces  the 
apparent  exceptions. 

As  instances  of  such  discoveries,  which  are  in  most  cases 
due  to  the  increasing  order  of  accuracy  made  possible  by 
improvements  in  measuring  instruments,  may  be  mentioned : 
first,  the  departure  of  actual  gases  from  the  simple  laws  of  the 
so-called  perfect  gas,  one  of  the  practical  results  being  the 
liquefaction  of  air  and  all  known  gases;  second,  the  discov- 
ery of  the  velocity  of  light  by  astronomical  means,  depend- 
ing on  the  accuracy  of  telescopes  and  of  astronomical  clocks ; 
third,  the  determination  of  distances  of  stars  and  the  orbits 
of  double  stars,  which  depend  on  measurements  of  the  order 
of  accuracy  of  one-tenth  of  a  second — an  angle  which  may  be 
represented  as  that  which  a  pin's  head  subtends  at  a  distance 
of  a  mile.  But  perhaps  the  most  striking  of  such  instances 
are  the  discovery  of  a  new  planet  by  observations  of  the  small 
irregularities  noticed  by  Leverier  in  the  motions  of  the 
planet  Uranus,  and  the  more  recent  brilliant  discovery  by 
Lord  Rayleigh  of  a  new  element  in  the  atmosphere  through 
the  minute  but  unexplained  anomalies  found  in  weighing  a 
given  volume  of  nitrogen.  Many  other  instances  might  be 
cited,  but  these  will  suffice  to  justify  the  statement  that  "  our 
future  discoveries  must  be  looked  for  in  the  sixth  place  of 
decimals."  It  follows  that  every  means  which  facilitates 
accuracy  in  measurement  is  a  possible  factor  in  a  future  dis- 
covery, and  this  will,  I  trust,  be  a  sufficient  excuse  for  bring- 


MicEoscoPE,  Telescope,  Inteeferometek     25 

ing  to  your  notice  the  various  methods  and  results  which 
form  the  subject-matter  of  these  lectures. 

Before  the  properties  of  lenses  were  known,  linear  meas- 
urements were  made  by  the  unaided  eye,  as  they  are  at  pres- 
ent in  the  greater  part  of  the  everyday  work  of  the  car- 
penter or  the  machinist;  though  in  many  cases  this  is 
supplemented  by  the  "touch"  or  "  contact"  method,  which 
is,  in  fact,  susceptible  of  a  very  high  degree  of  accuracy. 
For  angular  measurements,  or  the  determination  of  direc- 
tion, the  sight-tube  was  employed,  which  is  used  today  in  the 
alidade  and,  in  modified  form,  in  the  gun-sight  —  a  fact 
which  shows  that  even  this  comparatively  rough  means, 
when  properly  employed,  will  give  fairly  accurate  results. 

The  question  then  arises  whether  this  accuracy  can  be 
increased  by  sufficiently  reducing  the  size  of  the  apertures. 

The  answer  is:  Yes,  it  can,  but  only  up  to  a  certain  limit, 
beyond  which,  apart  from  the  diminution  in  brightness,  the 
diffraction  phenomena  just  described  intervene.  This  limit 
occurs  practically  when  the  diameter  of  two  openings  a 
meter  apart  has  been  reduced  to  about  two  millimeters,  so 
that  the  order  of  accuracy  is  about  ^-Xg-^Q-,  or  ygV^'  ^^^ 
measurements  of  angle.  Calling  ten  inches  the  limit  of  dis- 
tinct vision,  this  means  that  about  -^I-q  of  an  inch  is  the 
limit  for  linear  measurement.  An  enormous  improvement 
in  accuracy  is  effected  by  the  introduction  of  the  micro- 
scope and  telescope,  the  former  for  linear,  the  latter  for 
angular  measurements.  Both  depend  upon  the  property 
of  the  objective  lens  of  gathering  together  waves  from  a 
point,  so  that  they  meet  again  in  a  point,  thus  producing  an 
image. 

This  is  illustrated  in  Fig.  19.  A  train  of  plane  waves 
traveling  in  the  direction  of  the  arrows  encounters  a  convex 
lens.     The  velocity  is  less  in  glass,  and  since  the  lens  is 


26 


Light  Waves  and  Theie  Uses 


thickest  at  the  center,  the  retardation  is  greatest  there,  gradu- 
ally diminishing  toward  the  edge.  The  effect  is  to  change 
the  form  of  the  wave  front  from  a  plane  to  a  spherical  shell, 


^  ->  -> 


[5    o 


FIG.  19 


which  advances  toward  the  focus  at  O,  and  produces  at  this 
point  a  maximum  of  light,  which  is  the  image  of  the  point 
whence  the  waves  started. 

Fig.  20  illustrates  the  case  where  the  convex  waves 
diverging  from  a  luminous  point  O  are  changed  to  concave 
waves  converging  to  form  the  image  at  O ' . 

It  can  readily  be  shown  that  the  luminous  point  and  its 
image  are  in  the  same  line  with  the  center  of  the  lens  — 


o  < 


o' 


sufficiently  near  for  a  first  approximation.  Accordingly,  if 
we  take  separate  points  of  an  object,  we  can  construct  its 
image  by  drawing  straight  lines  from  these  through  the  cen- 
ter of  the  lens,  as  shown  in  Fig.  21.  The  size  of  the  image 
will  be  greater  the  greater  the  distance  from  the  lens,  so  that 


MiCKOscoPE,  Telescope,  Intekperometer     27 

the  magnification  is  proportional  to  the  ratio  of  the  distances 
from  object  and  image  respectively  to  the  center  of  the  lens ; 
hence  in  the  microscope  an  error  in  determining  the  position 
of  the  image  means  a  much  smaller  error  in  the  determination 


FIG.  21 

of  the  position  of  the  point  source.  This  error  could  be 
diminished  indefinitely  by  increasing  the  magnifying  power, 
were  it  not  for  the  attendant  loss  of  light  and  the  fact  that 
the  light  waves,  though  very  minute,  are  not  infinitesimally 
small.  In  fact,  the  same  diffraction  effects  again  limit  the 
possibility  of  indefinite  accuracy  of  measurement.  What, 
then,  is  the  new  limit? 

Let  p.  Fig.  22,  represent  the  center  of  the  geometrical 


FIG.  22 


image  of  a  luminous  point.  This  will  be  a  point  of  maximum 
brightness,  because  all  parts  of  the  concave  wave  which  con- 
verges toward  p  reach  this  point  at  the  same  time,  and  there- 
fore in  the  same  phase.  Let  us  consider  an  adjacent  point  q. 
The  parts  of  the  converging  wave  are  no  longer  at  equal 


28  Light  Waves  and  Their  Uses 

distances  from  this  point,  and  hence  will  not  arrive  in  the 
same  phase,  and  the  brightness  will  be  less  than  at  p.  At 
a  certain  distance  pg  there  will  be  no  light  at  all.  This 
occurs  when  the  difference  of  phase  between  the  extreme 
ray  and  the  central  ray  is  half  a  wave,  that  is,  calling 
the  wave  length  I,  when  cq  —  hq  —  ^  I;  for  these  two  pairs  of 
rays  destroy  each  other,  and  the  same  is  true  of  every  two 
such  pairs  of  rays. 

The  same  is  equally  true  of  every  point  about  p  at  this 
same  distance;  hence  there  will  be  a  dark  ring  about  the 
bright  image.  This  is  succeeded  by  a  bright  ring,  a  second 
dark  ring,  and  so  on. 

The  radius  of  the  first  dark  ring  may  be  calculated  as 
follows : 

Draw  qt  ai  right  angles  to  hp.  Then  cq  —  bq  =  ^l.  But 
cq  =  cp,  very  nearly,  and  cp  =  hp>,  and  bq  =  ht,  so  that 
6j3  —  hq—  pt  =  |-L 

But  the  triangles  pqi  and  phc  are  similar,  whence  pt  :  pq  = 
he  :  hp;  or,  calling  r  the  radius  of  the  first  dark  ring,  F 
the  focal  length  of  the  lens,  and  D  the  diameter  of  the  lens, 

r  —  j-l;   that  is,  the  radius  of  the  dark  ring  is  greater  than 

the  length  of  the  light  wave,  in  the  same  proportion  as  the 
focal  length  of  the  lens  is  greater  than  its  diameter.^  For 
example,  if  the  length  of  the  light  wave  be  taken  as  one 
fifty-thousandth  of  an  inch,  and  the  focal  length  of  the  lens 
as  one  hundred  times  the  diameter,  then  this  radius  will  be 
one  five-hundredth  of  an  inch  —  a  quantity  readily  percep- 
tible with  a  moderate  eyepiece.  The  lack  of  distinctness  of 
the  image  would  be  of  the  same  order,  and  would  be  further 
aggravated  by  greater  magnification,  resembling  a  drawing 
made  with  a  blunt  point. 

1  strictly,  this  is  about  ono-l'ourth  greater  on  account  of  the  fact  that  tlie  aper- 
ture is  circiilar  instead  of  rectangular. 


Microscope,  Telescope,  Inteeferometer     29 


In  most  cases  these  diffraction  rings  are  so  small  that  they 
escape  notice,  unless  the  air  is  unusually  quiet  and  the  lens 
exceptionally  good.  If  these  conditions  are  satisfied,  and 
the  instrument  is  focused  on  a  very  small  or  distant  bright 
object  (a  star,  or  a  pinhole  in  front  of  an  electric  arc),  the 
rings  are  readily  vis- 
ible with  a  sufficiently 
high-power  eye-piece. 
They  may  be  much 
more  readily  ob- 
served, however,  if  the 
ratio  of  diameter  to 
focal  length  be  di- 
minished by  placing 
a  circular  aperture 
before  the  lens.  The 
smaller  the  aperture, 


the  larger  will  be  the 


FIG.  23 


diffraction    rings. 
Fig.  23  is  a  photograph  of  the  phenomenon,  showing  the 
appearance  of  the  rings  when  the  diameter  of  a  lens  of  five 
meters'  focal  length  has  been  reduced  to  one  centimeter. 
In  the  case   of  a   telescope  the  corresponding   limiting 

angle  is  the  angle  subtended  by  r  at  the  distance  F,  i.  e.,  „, 

and  this,  by  the  formula,  is  the  same  as  the  angle  subtended 
by  the  light  wave  at  the  distance  D  —  the  diameter  of  the 
objective.  This  limiting  angle  for  a  five-inch  lens  would, 
therefore,  be  g-g-oVo-o  of  an  inch,  /.  e.,  about  the  size  of  a 
quarter  of  a  dollar  viewed  at  the  distance  of  a  mile.  This 
could  be  measured  to  within  one-fifth  of  its  value,  so  that 
the  accuracy  of  measurement  in  this  case  corresponds  to 
Ts-si-o-oo"  ^s  against  g-gVo"  without  the  lens;  /.  e.,  the  order  of 
accuracy  is  increased  about  five  hundred  times. 


30  Light  Waves  and  Theie  Uses 

For  a  microscope  it  will  be  simpler  to  proceed  a  little 
differently.  The  magnification  increases  as  the  object  ap- 
proaches the  front  of  the  objective  lens.  Suppose  it  is  almost 
in  contact.  The  waves  from  p  (Fig.  24)  reach  o  in  the  same 
phase,  but  those  from  q  reach  o  more  quickly  through  the 
upper  half  of  the  lens  than  through  the  lower  half.  Let 
the  difference  in  the  paths  qao  and  qho  be  /,  that  is,  one  of  the 
light  waves.     Then  there  will  be  darkness  at  o  so  far  as  the 


FIG.  24 

point  q  is  concerned;  i.  e.,  the  dark  ring  in  the  image  of  q 
will  lie  at  o  and  will  thus  coincide  with  the  bright  center  of  the 
image  of  p.  This  condition  of  affairs  corresponds  to  a  dis- 
placement pq  =  ^I.  Hence,  if  there  were  two  luminous 
points  at  a  distance  pg-  =  ^l  apart,  their  diffraction  images 
would  overlap  so  as  to  be  indistinguishable  from  each  other. 
Hence  ^l,  or  yo^iro  o~o  °^  ^^  inch,  is  the  "limit  of  resolution" 
in  any  microscope,  as  against  g^^-  of  an  inch  with  the  naked 
eye.  So  that  here  again  the  increase  in  accuracy  is  about 
four  hundred  times. 

These  theoretical  deductions  are  amply  confirmed  by 
actual  observation,  and  since  in  this  investigation  we  have 
supposed  a  theoretically  perfect  lens,  these  results  show 
that  our  present  microscopes  and  telescopes,  when  operated 
under  proper  conditions,  are  almost  perfect  instruments. 

Thus,  Fig.  25  shows  a  micro-photograph  of  the  specimen 
called  Amphipleura  pellucida,  whose  markings  are  about 


MicEoscoPE,  Telescope,  Inteefeeometeb     31 

100,000  to  the  inch.  This  is  about  the  theoretical  limit  for 
blue  light.  By  using  the  portion  of  the  spectrum  beyond 
the  violet  it  might  be  possible  to  go  still  farther. 


k      % 


FIG.  25 

Doubtless  by  a  much  higher  magnification  a  much  more 
accurate  setting  on  a  given  phase  of  the  fringes  could  be 
made,  and  hence  a  corresponding  increase  of  accuracy  of 
measurement  could  be  attained.  But  this  involves  a  great 
loss  of  light,  since  the  intensity  varies  inversely  as  the 
square  of  the  magnification.  Consequently,  even  with  a 
threefold  magnification  the  intensity  is  diminished  ninefold, 
so  that  it  would  be  difficult  to  see  the  image  unless  the  illumi- 


32  Light  Waves  and  Th?ir  Uses 

nation  were  so  powerful  as  to  endanger  the  specimen,  or  to 
introduce  temperature  variations  which  would  vitiate  the 
results  of  the  measurement. 

It  is  apparent  from  all  that  precedes  that  in  all  measure- 
ments by  the  microscope  or  the  telescope  we  are,  in  fact. 


FIG.  26 


making  use  of  the  interference  of  light  waves.  Let  us  see, 
then,  if  we  are  making  the  best  use  of  this  interference,  or 
whether  it  may  not  be  possible  to  increase  the  high  degree 
of  accuracy  already  attained. 

It  has  just  been  shown  that,  in  the  case  of  a  telescope,  the 
angular  magnitude  of  the  diffraction  rings,  and  with  this  the 
accuracy  of  measurement  of  the  position  of  the  luminous 
point,  depends  only  on  the  diameter  of  the  objective.  Now, 
the  form  of  the  fringes  will  of  course  vary  with  the  form  of 
the  aperture,  and  if  this  be  square  instead  of  circular,  the 
diffraction  image  will  be  represented  by  Fig.  26,  which  may 
be  compared  with  Fig.  23.  The  width  of  the  fringes  is  but 
little   altered,  while  there   is   a  perceptible  increase  in  dis- 


MiCEOscoPE,  Telescope,  Interferometer     33 


FIG.  27 


tinctness.  Let  the  middle  part  of  the  aperture  now  be  cov- 
ered up,  as  in  Fig.  27,  so  that  the  light  can  pass  through 
the  uncovered  portions,  a  and  b,  only. 
Fig.  28  shows  the  appearance  of  the 
fringes  in  this  case.  The  distribution  is 
somewhat  different,  but  the  distinctness 
is  considerably  increased,  so  that  the 
position  of  the  center  of  any  fringe  (the 
central  bright  fringe,  for  instance)  may 
be  measured  with  a  decided  increase  in 
accuracy.  The  utilization  of  the  two 
portions  of  a  lens,  at  opposite  ends  of  a  diameter,  converts 
the  telescope  or  microscope  into  an  inierfero meter . 

This  term  is  used  to  denote  any  arrangement  which  sepa- 
rates a  beam  of  light  into  two  parts  and  allows  them  to 
reunite  under  conditions  to  produce  interference.  The  path 
of  the  separated  pencils  may  be  varied  in  every  possible  way ; 

for  instance,  by  interposing  prisms 
or   mirrors,   provided    the    optical 
I  paths    are    nearly  equal   and    the 

angle  between  the  two  final  direc- 
tions very  small.  The  first  condi- 
tion is  essential  only  when  the  light 
is  not  homogeneous.  The  reason 
will  be  apparent  when  it  is  remem- 
bered that  the  width  of  the  inter- 
ference bands  depends  on  the  wave 
length  of  the  light  employed.  If 
the  light  is  composite,  as  in  the 
case  of  white  light,  each  component 
will  form  interference  bands  whose  width  is  proportional  to 
the  wave  length. 

This  is  illustrated  in  Fig.  29,  where  the  fringes  due  to 
red,  yellow,  and  blue  light  respectively  are  separated.      In 


11 


FIG.  28 


34 


Light  Waves  and  Their  Uses 


the    actual    experiment,  however,   they   are  all  superposed. 
At  the  middle  point,  where  the  two  paths  are  equal,  all  the 

colors  will  be  superposed,  the  re- 
sult being  a  ivhite  central  band. 
At  no  other  point  will  this  be  true, 
and  the  result  will  be  a  series  of 
colored  fringes  symmetrically  dis- 
posed about  the  central  white 
fringe,  the  succession  of  colors 
being  exactly  the  same  as  in  the 
case  of  thin  films  (cf.  Plate  II). 

The  breadth  of  the  fringes  is 
determined  by  the  smallness  of  the 
angle  under  which  the  two  pencils 
meet.  This  is  shown  in  Fig.  30. 
In  the  right-hand  figure  the  angle 
between  the  pencils  is  smaller  than 
in  the  other,  while  the  breadth  of  the  fringes  is  correspond- 
ingly greater  in  the  former  than  in  the  latter.     The  exact 


FIG.  29 


FIG.  .30 


relation  is  readily  obtained.  We  have  only  to  note  that  ac 
is  the  wave  length  I  (very  nearly)  and  he  is  (very  nearly)  the 
width  6  of  a  fringe;  whence,  if  c  is  the  very  minute  angle 


MicEosooPE,  Telescope,  Interferometer     35 

at  6  (which  is  the  same  as  the  angle  between  the  directions 

of  the  interfering  pencils),   b  =  -;   or,  in  other  words,  the 

width  of  the  fringes  is  proportional  to  the  wave  length  of  the 
light,  and  inversely  proportional  to  the  angle  between  the 
pencils. 

Thus,  if  the  pencils  converge  from  two  apertures  a 
quarter  of  an  inch  apart,  and  meet  at  a  screen  ten  feet  away, 
the  breadth  of  the  fringes  will  be  one-hundredth  of  an  inch. 

The  importance  of  using  a  very  small  angle  will  be  noted. 


FIG.  31 


In  this  simple  form  of  interferometer  the  angle  can  be 
made  small  only  by  bringing  the  two  apertures  very  near 
together,  which  seriously  diminishes  the  efficiency  of  the 
instrument ;  or  by  increasing  the  distance  from  the  openings 
to  the  fringes,  or  by  using  a  high  magnification,  which  en- 
feebles the  light,  already  very  faint  in  consequence  of  having 
to  start  from  a  pinhole  or  a  narrow  slit  s  (Fig.  31)  and 
to  pass  through  the  narrow  apertures  a  and  6.  There  is, 
therefore,  but  little  advantage  in  this  form  of  interferometer 
over  the  corresponding  older  analogues  (microscope  and 
telescope). 

An  important  improvement  may  be  effected  by  bending 
one  or  both  the  rays  aj),  hp  by  reflections  in  such  a  way  as  to 
diminish  the  angle  at  p,  as  shown  in  Fig.  32. 

A  further  improvement  is  effected  by  replacing  the  aper- 
tures a  and  h  by  mirrors;  and,  finally,  by  replacing  the  slit 


30 


Light  Waves  and  Theie  Uses 


s  by  a  plane  surface.  The  interferometer  is  now  changed 
into  the  form  illustrated  in  Fig.  33.  It  will  now  be 
noted  that  the  source  need  no  longer  be  a  point  or  a  slit, 
but  may  be  a  broad  flame ;  and  the  object  whose  position  is  to 


FIG.  32 

be  measured  is  no  longer  a  fine  line  or  a  slit,  but  a  flat  surface. 
The  width  of  the  fringes  may  be  made  as  great  as  we  please 
without  any  sacrifice  in  the  brightness  of  the  light.  The  corre- 
sponding increase  in  accuracy  is  from  twenty  to  one  hundred 
fold.  We  may  conveniently  restrict  the  term  interferometer  to 
this  arrangement,  in  which  the  division  and  the  union  of  the 
pencils  of  light  are  effected  by  a  transparent  plane  parallel 
plate.     It  is  important  to  note  that  the  path  of  the  two  pen- 


FIG.  33 


cils  after  their  separation  by  the  first  plate  is  entirely  imma- 
terial; for  example,  either  or  both  pencils  may  suffer  any 
number  of  reflections  or  refractions  before  they  are  reunited 
by  the  second  plate,  without  affecting  in  any  essential  point 
the  efficiency  of  the  interferometer,  provided  that  the  differ- 


Microscope,  Telescope,  Interferometer     37 

ence  in  the  patli  of  the  two  pencils  is  not  too  great,  and 
provided  that  the  two  pencils  are  reunited  at  a  sufficiently 
small  angle.     By  altering  these  conditions   of  reflection  or 


'-^■-  V- 


\; 


-  -X 


FIG.  34 


38 


Light  Waves  and  Their  Uses 


refraction  we   may   obtain    a  very  considerable  number  of 
variations  of  form,  as  illustrated  in  Figs.  34,  35. 

One  of  these  types,  enlarged  in  Fig.  36,  has  been  arranged 


.--/ 


FIG.  35 


Microscope,  Telescope,  Interferometer     39 


in  such  a  way  as  to  show  the  extreme  delicacy  of  the  inter- 
ferometer in  measuring  exceedingly  small  angles.  For 
this    purpose    two    of   the 


D 


O 


FIG.  3; 


mirrors,  C  and  i),  have  been 

mounted  on  a  piece  of  steel 

shafting  P  two  inches  in 

diameter    and    six    inches 

long.     When    the    length 

of    the    paths  of    the  two 

pencils    is    the  same    to 

within  a  few  hundred  thou-  ^^ 

sandths  of  an  inch,  the  in- 
terference fringes  in  white 

light  are  readily  observed, 

or  may  be  projected  on  the 

screen.      If,  now,  the  steel  shafting  be  twisted,  one  of  the 

paths  is  lengthened  and  the  other  diminished,  and  for  every 

movement  of  one 
two-hundred-thou- 
sandth of  an  inch 
there  would  be  a 
motion  of  the 
fringes  equal  to 
the  width  of  a 
fringe.  Now,  tak- 
ing the  end  of  the 
steel  shafting  be- 
tween thumb  and 
forefinger,  the  ex- 
ceedingly small 
force  which  may 
thus  be  applied 
in  this  way  is 
FIG.  -s]  sufficient   to  twist 


40 


Light  Waves  and  Theie  Uses 


FIG.  38 


the  solid  steel  shafting  through  an  angle  which  is  very 
readilv  observed  by  the  movement  of  the  fringes  across  the 
field. 

The  form  of  interferometer  which  has  proved  most  gen- 
erally useful  is  that  shown  in  Fig.  38.     The    light    starts 

I ,  from  source  S  and  separates  at 

the  rear  of  the  plate  A,  part  of 
it  being  reflected  to  the  plane 
mirror  C,  returning  exactly, 
on  its  path  through  A,  to  O, 
where  it  may  be  examined  by  a 
telescope  or  received  upon  a 
screen.  The  other  part  of  the 
ray  goes  through  the  glass  plate 
A,  passes  through  B,  and  is  re- 
flected by  the  plane  mirror  D, 
returns  on  its  path  to  the  starting-point  A,  where  it  is 
reflected  so  as  nearly  to  coincide  with  the  first  ray.  The 
plane-parallel  glass  B  is  introduced  to  compensate  for  the 
extra  thickness  of  glass  which  the  first  portion  of  the  ray 
has  traversed  in  passing  twice  through  the  plate  A.  With- 
out it  the  two  paths  would  not  be  optically  identical,  because 
the  first  would  contain  more  glass  than  the  second. 

Some  light  is  reflected  from  the  front  surface  of  the  plate 
A,  but  its  effect  may  be  rendered  insignificant  by  covering 
the  rear  surface  of  A  with  a  coating  of  silver  of  such  thick- 
ness that  about  equal  portions  of  the  incident  light  are 
reflected  and  transmitted. 

The  plane-parallel  plates  A  and  B  are  worked  originally 
in  a  single  piece,  which  is  afterward  cut  in  two.  The  two 
pieces  are  placed  parallel  to  each  other,  thus  insuring  exact 
equality  in  the  two  optical  paths  AC  and  AD. 

The  foregoing  principles  are  applied  in  concrete  form  in 
the  instrument  shown  in  Figs.  39,  40.     A  rigid  casting  serves 


Microscope,  Telescope,  Interferometer     41 


as  the  bed  of  the  instrument.  One  end  of  this  bed  has 
fastened  to  it  a  heavy  metal  plate  H,  which  carries  the 
three  glass  plates  A,  D,  and  B.  The  plate  A  is  held  in 
a  metal  frame  which  is  rigidly  fastened  to  the  plate  H. 
The  frame  which  holds  B  can  be  turned  slightly  about  a 
vertical  axis  to  allow  of  adjust- 
ing B  so  that  it  is  parallel  to  A. 
The  mirror  D  is  held  by  springs 
against  three  adjusting  screws 
which  are  set  in  a  vertical  plate 
attached  to  the  end  of  the  plate 
H.  Both  C  and  D  are  silvered 
on  their  front  faces.  The  frame 
which  holds  the  mirror  C  is 
firmly  mounted  on  a  metal  slide 
which  can  be  moved  by  the  screw 
S  along  the  ways  EF.  One  very 
essential  feature  of  the  apparatus 
is  that  these  ways  shall  be  so  true 
that  the  mirror  C  shall  remain 
parallel  to  itself  as  it  is  moved 
along.  The  accuracy  of  the  ways 
must  be  so  great  that  the  greatest 
angle  through  which  the  mirror 
C  turns  in  passing  along  them  is 
less  than  one  second  of  an  arc. 
This  accuracy  cannot  be  attained  by  the  instrument  maker, 
but  the  final  grinding  must  be  done  by  the  investigator 
himself. 

To  adjust  the  instrument  so  that  fringes  are  formed,  a 
small  object  like  a  pin  is  held  between  the  source  and  the 
plate  A.  Two  images  of  this  pin  will  be  seen  by  an  ob- 
server at  O — one  formed  by  the  light  which  is  reflected  from 
C,  and  the  other  by  that  reflected  from  D.     The  fringes  in 


FIG.  39 


42 


Light  Waves  and  Their  Uses 


monochromatic  light  will  appear  when  these  two  images 
have  been  made  to  coincide  with  the  help  of  the  adjusting 
screws  ss.  The  fringes  in  white  light  appear  only  when  the 
lengths  of  the  two  paths  AD  and  AC  are  the  same.     The 


1 

BHi 

1 

■j 

1 

1 

FIG.  40 


width  and  the  position  of  the  fringes  in  the  field  of  view 
can  be  varied  by  slightly  moving  the  adjusting  screws.  We 
shall  have  occasion  to  discuss  this  particular  form  of  inter- 
ferometer in  a  subsequent  lecture. 

SUMMAEY 

1.  The  objection  to  the  wave  theory  of  light,  that  light 
moves  in  straight  lines  while  sound  waves  can  bend  around 
an  obstacle,  is  shown  to  be  groundless,  since  we  have  seen 
that  if  the  sound  waves  are  sufficiently  short  they  cast  a 
sound  shadow,  while  by  devices  which  take  into  account  the 


MiCEOscoPE,  Telescope,  Interferometer     43 

extreme    minuteness  of    light  waves  their  bending  around 
obstacles  may  be  readily  observed. 

2.  The  extreme  minuteness  of  light  waves  renders  it  pos- 
sible to  utilize  the  microscope  and  the  telescope  as  instru- 
ments of  great  precision.  These  instruments  depend  on  the 
property  of  the  objective  of  gathering  together  waves  from 
a  point  so  that  they  are  concentrated  in  the  diffraction  pat- 
tern which  is  called  the  image. 

'  3.  The  accuracy  of  measurement  is  still  further  increased 
■by  modifying  the  telescope  or  microscope  so  as  to  utilize 
only  two  pencils,  thus  converting  these  instruments  into 
interferometers. 

4.  By  the  device  of  separating  the  two  pencils  and 
reuniting  them  by  reflections  from  plane-parallel  surfaces, 
the  fringes  may  be  made  as  large  as  we  please  without 
diminishing  the  brightness  of  the  light,  and  hence  the  ac- 
curacy of  measurement  may  be  correspondingly  increased. 


LECTUEE    III 

APPLICATION    OF    INTERFERENCE    METHODS    TO    MEAS- 
UREMENTS OF  DISTANCES  AND  ANGLES 

In  the  last  lecture  we  considered  the  limitations  of  the 
telescope  and  microscope  when  used  as  measuring  instru- 
ments, and  showed  how  they  may  be  transformed  so  that  the 
diffraction  and  interference  fringes  which  place  the  limit 
upon  their  resolving  power  may  be  made  use  of  to  increase 
the  accuracy  of  measurements  of  length  and  of  angle.  We 
have  named  these  new  forms  of  instrument  interferometers 
and  illustrated  many  of  the  forms  in  which  they  may  be  made. 

It  has  been  found  that  the  particular  form  of  interfer- 
ometer described  on  p.  40  is  the  most  generally  useful,  and 
the  principal  subject  of  this  lecture  will  be  to  illustrate  the 
applications  which  have  already  been  made  of  this  instrument. 

But  before  passing  to  the  first  application  of  the  interfer- 
ometer, we  may  make  a  little  digression,  and  consider  briefly 
the  two  theories  which  have  been  proposed  to  account  for  the 
various  phenomena  of  light.  One  of  these  is  the  undulatory 
theory,  which  has  already  been  explained;  the  other  is  the 
corpuscular  theory,  which  for  a  long  time  held  its  ground 
against  the  undulatory  theory,  principally  in  consequence  of 
the  support  of  Newton. 

The  corpuscular  theory  supposes  that  a  luminous  body 
shines  in  virtue  of  the  emission  of  minute  particles.  These 
corpuscles  are  shot  out  in  all  directions,  and  are  supposed  to 
produce  the  sensation  of  vision  when  they  strike  the  retina. 
The  corpuscular  theory  was  for  a  long  time  felt  to  be  unsatis- 
factory because,  whenever  a  new  fact  regarding  light  was 
discovered,  it  was  always  necessary  to  make  some  supplemen- 

44 


Application  of  Interference  Methods      45 

tary  hypothesis  to  strengthen  the  theory ;  whereas  the  undu- 
latory  theory  was  competent  to  explain  everything  without 
the  addition  of  extra  hypotheses.  Nevertheless,  Newton 
objected  to  the  undulatory  theory  on  the  ground  that  it  was 
difficult  to  conceive  that  a  medium  which  offers  no  resistance 
to  the  motion  of  the  planets  could  propagate  vibrations  which 
are  transverse  (and  we  know  that  the  light  vibrations  are  trans- 
verse because  of  the  phenomena  of  polarization),  for  such 
vibrations  can  be  propagated  only  in  a  medium  which  has  the 
properties  of  a  solid.  Thus,  if  the  end  of  a  metal  rod  be 
twisted,  the  twist  travels  along  from  one  end  to  the  other 
with  considerable  velocity.  If  the  rod  were  made  of  sealing 
wax,  the  twist  would  rapidly  subside.  If  such  a  rod  could 
be  made  of  liquid,  it  would  offer  virtually  no  elastic  resist- 
ance to  such  a  twist. 

Notwithstanding  this,  the  medium  which  propagates 
light  waves,  and  which  was  supposed  to  resist  after  the 
fashion  of  an  elastic  solid,  must  offer  no  appreciable  resist- 
ance to  such  enormous  velocities  as  those  of  the  planets 
revolving  in  their  orbits  around  the  sun.  The  earth,  for 
example,  moves  with  a  velocity  of  something  like  twenty 
miles  in  a  second,  has  been  moving  at  that  rate  for  millions 
of  years,  and  yet,  as  far  as  we  know,  there  is  no  considerable 
increase  in  the  length  of  the  year,  such  as  would  result 
if  it  moved  in  a  resisting  medium.  There  are  other 
heavenly  bodies  far  less  dense  than  the  earth,  e.  g.,  the 
comets,  and  it  seems  almost  incredible  that  such  enormously 
extended  bodies  with  such  an  exceedingly  small  mass  should 
not  meet  with  some  resistance  in  passing  throug^h  their 
enormous  orbits.  The  result  of  such  resistance  would  be 
an  increase  in  the  period  of  revolution  of  the.  comets,  and 
no  such  increase  has  been  detected.  We  are  thus  required 
to  postulate  a  medium  far  more  solid  than  steel  and  far  less 
viscous  than  the  lightest  known  gas. 


40  Light  Waves  and  Their  Uses 

These  two  suppositions  are  possibly  not  as  inconsistent 
as  they  may  at  first  seem  to  be,  for  we  have  a  very  important 
analogy  to  guide  us.  Consider,  for  example,  shoemaker's 
wax,  or  pitch,  or  asphaltum.  These  substances  at  ordinary 
temperatures  are  hard,  brittle  solids.  If  you  drop  them,  they 
break  into  a  thousand  pieces ;  if  you  strike  them  (so  lightly 
that  they  do  not  break),  they  emit  a  sound  which  corresponds 
to  the  transverse  vibrations  of  a  solid.  If,  however,  we  place 
one  of  these  substances  on  an  inclined  surface,  it  will  gradually 
flow  down  the  incline  like  a  liquid.  Or  if  we  support  a  cake 
of  shoemaker's  wax  on  corks  and  place  bullets  on  its  upper 
surface,  after  a  time  the  bullets  will  have  sunk  to  the  bottom, 
and  the  corks  will  be  found  floating  on  top.  So  in  these 
cases  we  have  a  gross  and  imperfect  illustration  of  the  co- 
existence of  apparently  inconsistent  properties  such  as  are 
required  in  our  hypothetical  medium.'  Nevertheless,  it 
seemed  impossible  to  Newton  to  conceive  a  medium  with 
such  incompatible  properties,  and  this  was,  as  stated  above, 
a  serious  obstacle  in  the  way  of  his  accepting  the  undula- 
tory  theory.  There  were  others,  which  need  not  now  be 
mentioned. 

For  a  long  time  after  the  various  modifications  that  the 
corpuscular  theory  had  to  receive  had  been  made,  both  theo- 
ries were  actually  capable  of  explaining  all  the  phenomena 
then  known,  and  it  seemed  impossible  to  decide  between 
them  until  it  was  pointed  out  that  the  corpuscular  theory 
made  it  necessary  to  suppose  that  light  traveled  faster  in  a 
denser  medium,  such  as  water  or  glass,  than  it  does  in  a 
rarer  medium,  such  as  air;  while  according  to  the  undulatory 
theory  the  case  is  reversed.  We  may  illustrate  briefly  the 
two  cases:  No  matter  what  theory  we  accept,  it  is  an 
observed  fact   that  refraction  takes  place  when  light  passes 

'The  specialization  of  the  undulatory  theory  known  as  the  electro-magnetic 
theory  floes  not  remove  this  difficulty;  for  it  is  even  more  difficult  to  account  for 
the  properties  of  a  medium  which  is  the  seat  of  electric  and  magnetic  forces. 


Application  of  Interference  Methods      47 


from  a  denser  to  a  rarer  medium,  and  consists  in  a  bending 
of  the  incident  ray  toward  the  normal  to  the  surface  of  the 
denser  medium.  Suppose  we  have  a  plate  of  glass,  for  exam- 
ple, and  a  ray  of  light  falling  upon  the  surface  in  any  direc- 
tion. According  to  the  corpuscular  theory,  the  substance 
below  the  surface  exerts 
an  attraction  upon  the 
light  corpuscles.  Such 
attraction  can  act  only 
in  the  direction  of  the 
normal.  If  we  separate 
it  into  two  components, 
one  in  the  surface  and 
one  normal  to  it,  the 
normal  one  will  be  in- 
creased. These  two  com- 
ponents might  be  repre- 
sented by  OA  and  OB  in  Fig.  41,  and  the  resultant  of  the 
two  would  be  OC.  In  consequence  of  the  presence  of  the 
denser  medium,  the  normal  component  of  the  velocity  of  the 
particle  is  increased,  and  the  resultant  is  now  OC ,  which  is 
greater  than  OC. 

Let  us  next  consider  refraction  according  to  the  wave 
theory.  A  wave  front  ah  (Fig.  42)  is  approaching  the  surface 
ac  of  a  denser  medium  in  the  direction  bo.  This  direction  is 
changed  by  refraction  to  ce,  and  the  corresponding  direction 
of  the  new  wave  front  is  cd.  During  the  time  that  the  wave 
ah  moves  through  the  distance  he  in  the  rarer  medium,  it 
moves  through  the  smaller  distance  ad  in  the  denser.  Thus 
the  results,  according  to  the  two  theories,  are  exactly  reversed. 

Hence,  if  we  could  measure  the  enormous  speed  of  light  — 
about  400,000  times  as  great  as  that  of  a  rifle  bullet — it  would 
be  possible  to  put  the  two  theories  to  the  test.     In  order  to 


48 


Light  Waves  and  Their  Uses 


accomplisli  this  we  must  compare  the  velocities  of  light  in 
air  and  in  some  denser,  transparent  medium  —  say  water. 
Now,  the  greatest  length  of  a  column  of  water  which  still 
permits  enough  light  to  pass  to  enable  us  to  measure  the 
very  small  quantities  involved  is  something  like  thirty  feet. 

We  should  therefore 
have  to  determine  the 
time  it  takes  the  light 
to  pass  through  thirty 
feet  of  water,  at  the 
rate  of  150,000  miles 
a  second.  This  inter- 
val of  time  is  of  the 
order  of  one  twenty- 
millionth  of  a  second. 
But  we  must  measure 
a  time  interval  even 
smaller  than  this,  for 
we  have  to  distinguish  between  the  velocity  in  water  and  the 
corresponding  velocity  in  the  air,  /.  e.,  to  determine  the  dif- 
ference between  two  time  intervals,  each  of  which  is  of  the 
order  of  one  twenty-millionth  of  a  second.  This,  at  first  sight, 
seems  beyond  the  possibility  of  any  physical  experiment;  but, 
notwithstanding  this  exceedingly  small  interval  of  time,  by 
the  combined  genius  of  Wheatstone,  Arago,  Foucault,  and 
Fizeau  the'  problem  has  been  successfully  solved.  The 
method  proposed  by  Wheatstone  for  measuring  the  velocity 
of  electricity  was  this :  A  mirror  was  mounted  so  that  it  could 
be  revolved  about  an  axis  parallel  to  its  surface  at  a  very 
high  rate,  and  the  light  from  the  spark  produced  by  the  dis- 
charge of  a  condenser  was  allowed  to  fall  on  the  mirror.  The 
images  of  two  sparks  were  observed  in  the  revolving  mirror; 
the  second  spark  passed  after  the  electric  current  which  pro- 
duced it  had  passed  through  a  considerable  length  of  wire  — 


FIG.  42 


Application  of  Inteefekence  Methods       49 

perhaps  several  miles;  the  first,  after  it  had  passed  through 
only  a  few  feet  of  wire.  If  the  mirror  in  this  interval  had 
turned  through  a  perceptible  angle,  the  reflected  light  would 
have  moved  through  double  that  angle;  and,  knowing  the 
velocity  of  rotation  of  the  mirror,  and  measuring  this  small 
angle,  the  velocity  of  electricity  could  be  determined.  Arago 
thought  this  same  method  might  be  adapted  to  the  measure- 
ment of  the  velocity  of  light. 


M 


FIG.  43 

The  principle  of  Arago's  method  may  be  illustrated  as 
follows:  Suppose  we  have  a  mirror  i?  (Fig.  43),  revolving 
in  the  direction  of  the  arrows,  s  is  a  spark  from  a  con- 
denser, which  sends  light  directly  to  the  mirror  B,  and  also 
to  the  distant  mirror  M,  whence  it  returns  to  R,  and  both 
rays  are  reflected  in  the  direction  s^.  If,  however,  the  light 
takes  an  appreciable  time  to  pass  from  s  to  ill^  and  back, 
this  light  will  reach  the  mirror  R  later,  and  the  mirror  will 
have  turned  in  the  interval  so  as  to  reflect  the  light  to  So- 
li the  angle  s-^Rso  can  be  measured,  the  angJe  through 
which  the  mirror  moves  is  one-half  as  great ;  and,  knowing 
the  speed  of  the  mirror,  we  know  also  the  time  it  takes  to 
turn  through  this  angle ;  and  this  is  the  time  required  for 
light  to  traverse  twice  the  distance  sil/,  whence  the  velocity 
of  light. 

The  principle  of  Arago's  method  is  sound,  but  it  would 
be  extremely  difficult  to  carry  it  into  practice  without  an 
important  modification,  due  to  Foucault,  which  is  illustrated 


50  Light  Waves  and  Their  Uses 

in  Fig.  44.  Light  from  a  source  s  falls  on  the  revolving  mir- 
ror H,  and  by  means  of  a  lens  L  forms  an  image  of  s  at  the 
surface  of  a  large  concave  mirror  M.  The  light  retraces  its 
path  and  forms  an  image  which  coincides  with  s  if  the  mirror 
H  is  at  rest  or  is  turning  slowly.  When  the  rotation  is  suf- 
ficiently rapid  the  image  is  formed  at  s^,  and  the  displace- 
ment ssi  is  readily  measured. 


If  the  distance  LM  is  occupied  by  a  column  of  water, 
the  displacement  would  be  less  if  the  velocity  of  light  is 
greater  in  water  than  in  air,  as  it  should  be  according  to  the 
corpuscular  theory ;  and  if  the  undulatory  theory  is  correct, 
the  displacement  would  be  greater.  Foucault  found  the 
displacement  greater,  and  thus  the  corpuscular  theory  re- 
ceived its  death-blow. 

It  remained  for  subsequent  experiment  to  determine 
whether  the  undulatory  theory  was  true,  because  it  was  not 
sufficient  to  show  that  the  velocity  was  smaller  in  water;  it 
was  necessary  to  show  that  the  ratio  of  the  two  velocities 
was  equal  to  the  index  of  refraction  of  the  water,  which  is 
1.33.  Experiments  showed  that  the  ratio  of  the  two  veloci- 
ties is  almost  identical  with  this  number,  thus  furnishing  an 
important  confirmation  of  the  undulatory  theory. 

Ordinarily  the  index  of  refraction  is  found  by  measuring 
the  amount  of  bending  which  a  beam  of  light  experiences  in 


Application  of  Intekference  Methods       51 


FIG.  45 


passing  from  air  into  the  medium  in  question.  But  if  this 
number  is  identical  with  the  ratio  of  the  velocities,  the 
index  would  evidently  be  determined  if  we  knew  the  ratio 
of  the  wave  lengths,  since  the  wave  lengths  are  also  propor- 
tional to  the  velocities.  This  can  be  obtained  by  the  inter- 
ferometer. In  fact,  the  origi- 
nal name  of  the  instrument  is 
"interferential  refractometer," 
because  it  was  first  used  for 
this  purpose  by  Fresnel  and 
Arago  in  1816.  This  name, 
however,  is  as  cumbersome  as 
it  is  inappropriate,  for,  as  we 
shall  see,  the  range  of  useful- 
ness of  the  instrument  is  by  no  means  limited  to  this  sort 
of  measurement. 

The  interferometer  being  adjusted  for  white  light,  the 
colored  interference  fringes  are  thrown  on  the  screen.  If, 
now,  the  number  of  waves  in  one  of  the  paths  be  altered  by 
interposing  a  piece  of  glass,  the  adjustment  will  be  disturbed 
and  the  fringes  will  disappear;  for  the  difference  of  path 
thus  introduced  is  several  hundreds  or  thousands  of  waves; 
and,  as  shown  in  the  preceding  lecture,  the  fringes  appear 
in  white  light  only  when  the  difference  of  path  is  very  small. 

The  exact  number  of  waves  introduced  can  readily  be 

shown  to    be  2{n— l)-y  that  is,  twice  the  product  of  the 

index  less  unity  by  the  thickness  of  the  glass  divided  by  the 
length  of  the  light  wave.  Thus,  if  the  index  of  the  glass 
plate  is  one  and  one-half  and  its  thickness  one  millimeter, 
and  the  wave  length  one-half  micron,  the  difference  in  path 
would  be  two  thousand  waves. 

Let  us  take,  therefore,  an  extremely  thin  piece  of  mica, 
or    a    glass  film  such   as    may  be   obtained    by   blowing   a 


52 


Light  Waves  and  Their  Uses 


FIG.  46 


bubble  of  glass  till  it  bursts.  Covering  only  half  the  field  with 
the  film,  the  fringes  on  the  corresponding  side  are  shifted  in 
position,  as  shown  in  Fig.  45,  and  the  number  of  fringes  in 
the  shift  is  the  number  of  waves  in  the  difference  of  path, 
from  which  the  index  can  be  calculated  by  the  formula.^ 

The  interferometer  is  particu- 
larly well  adapted  for  showing  very 
slight  differences  in  the  paths  of 
the  two  interfering  pencils,  such, 
for  instance,  as  are  produced  by 
inequalities  in  the  temperature  of 
the  air.  The  heat  of  the  hand  held 
near  one  of  the  paths  is  quite  suf- 
ficient to  cause  a  wavering  of  the 
fringes;  and  a  lighted  match  pro- 
duces contortions  such  as  are  shown 
in  Fig.  46.  The  effect  is  due  to  the  fact  that  the  density 
of  the  air  varies  with  the  temperature;  when  the  air  is  hot 
its  density  diminishes,  and  with  it  the  refractive  index. 

It  follows  that,  if  such  an  experiment  were  tried  under 
proper  conditions,  so  that  the  displacement  of  the  interfer- 
ence fringes  were  regular  and  could  be  measured — which 
means  that  the  temperature  is  uniform  throughout — then  the 
movement  of  the  fringes  would  be  an  indication  of  tempera- 
ture. Comparatively  recently  this  method  has  been  used  to 
measure  very  high  temperatures,  such  as  exist  in  the  interior 
of  blast  furnaces,  etc. 

In  "one  of  the  preceding  lectures  an  image  of  a  soap  film 
was  thrown  on  the  screen,  and  it  was  shown  that  the  thick- 
ness of  the  film  increased  regularly  from  top  to  bottom, 
and  that  where  the  thickness  was  sufficiently  small  the 
interference  fringes  enable  us  to  deduce  the  thickness  of  the 

1  For  quantitative  measurements  it  is  necessary  to  employ  monochromatic  lislit. 
The  shifting  of  the  central  band  of  the  colored  frinRes  in  white  light  does  not  give 
even  an  approximately  accurate  result. 


Application  of  Intekfeeence  Methods       53 

film.  It  was  also  shown  that  at  the  top  of  the  film,  where 
the  thickness  was  very  small,  a  black  band  appears,  its  lower 
edge  being  sharply  defined  as  though  there  were  here  a  sud- 
den change  in  thickness,  as  illustrated  in  Fig.  47. 

Now,  this  "black  spot"  may  be  observed  sufficiently  long 
to  measure  the  displacement  produced 
in  interference  fringes  when  the  film 
is  placed  in  the  interferometer.  It 
is  probable  that  over  the  area  of  the 
"black  spot"  the  two  surfaces  of  the 
film  are  as  near  together  as  possible; 
and  if  the  water  is  made  up  of  mole- 
cules, there  are  very  few  molecules 
in  this  thickness  —  possibly  only  two 

.  FIG.  47 

— SO    that    a    measurement    of    this 

thickness  would  give  at  least  an  upper  limit  to  the  distance 

between  the  molecules. 

A  soap  solution  of  slightly  different  character  from  that 
used  in  the  last  lecture  is  more  serviceable  for  this  purpose.' 
With  such  a  solution  the  film  lasts  a  remarkably  long  time. 
It  is  interesting  to  note  that  some  time  after  the  "black 
spot "  has  formed,  portions  of  its  surface  reflect  even  less 
light  than  the  rest,  and  these  portions  gradually  increase 
in  size  and  number  till  the  whole  surface  almost  entirely 
vanishes. 

It  is  found  on  placing  such  a  film  as  this  in  the  inter- 
ferometer that  there  is  no  appreciable  change  in  the  fringes. 
The  film  is  so  thin  that  we  cannot  observe  any  displacement 
at  all ;  if  we  place  two  films  in  the  interferometer,  the  dis- 
placement should  be  twice  as  great ;  but  even  then  it  is  inap- 
preciable. To  obtain  a  measurable  displacement  it  was 
found  necessary  to  use  fifty  such  films.     The  arrangement 

iThis  solution  is  made  of  caustic  soda  1  gm.,  oleic  acid  7  gm.,  dissolved  in  600 
CO.  of  water. 


54 


Light  Waves  and  Theik  Uses 


of  the  interferometer  for  this  experiment'  is  shown  in  Fig.  48. 
The  films  are  introduced  in  the  path  AC,  as  indicated  at 

F.  Yet  even  fifty  films 
produced  a  displacement 
of  only  about  half  a 
fringe,  as  shown  in  Fig. 
49.  Since  the  light 
passed  through  each  film 
twice,  this  displacement 
of  half  a  fringe  is  what 
would  be  produced  by  a 
single  passage  through 
one  hundred  films.  One 
film  would  therefore 
produce  a  displacement 
of  one  two-hundredths 
of  a  fringe.  A  simple  calculation  tells  us  that  the  correspond- 
ing distance  between  the  water  molecules  is  not  greater  than 
six  millionths  of  a  millimeter.  It  may  be  much  less  than  this. 
The  interferometer  is  especially  useful  whenever  it  is 
necessary  to  measure  small  changes  in  distance  or  angle. 
One  rather  important  instance  of 
such  a  measure  is  that  of  coefiicient 
expansion.  Most  bodies  expand 
with  heat — certainly  a  very  small 
quantity:  one  or  two  parts  in  ten 
thousand  for  a  change  of  tempera- 
ture of  a  single  degree. 


FIG.  48 


m 


FIG.  49 


In  some  cases  it  may  be  neces- 
sary to  experiment   upon   a  very 
small  specimen  of  the  material  in 
question,  and  in  such  cases  the  whole  change  to  be  measured 
may  be  of  the  order  of  a  ten-thousandth  part  of  an  inch  — 

1  E.  S.  JonoNNOTT,  Phil.  Mag.  (5),  Vol.  XLVII  (1899),  p.  501. 


Application  of  Interference  Methods      55 


a  quantity  requiring  a  good  microscope  to  perceive;  but 
such  a  quantity  is  very  readily  measured  by  the  inter- 
ferometer. It  means  a  displacement  amounting  to  several 
fringes,  and  this  displacement  may  be  measured  to  within  a 
fiftieth  of  a  fringe  or  less ;  so  that  the  whole  displacement 
may  be  measured  to 
within  a  fraction  of  1  per 
cent.  Of  course,  with 
long  bars  the  attainable 
degree  of  accuracy  is  far 
greater. 

Figs.  50  and  51  rep- 
resent a  piece  of  appa- 
ratus designed  by  Pro- 
fessors Morley  and 
Rogers,^  based  on  this 
principle,  b  and  c  (Fig. 
50)  are  the  two  plane- 
parallel  plates  of  the  in- 
terferometer, and  the  two 
mirrors  are  at  a  and  a' .  Each  mirror  is  divided  into  two 
halves  as  at  aa,  so  that  a  motion  of  each  end  of  the  bar  to 
be  tested  can  be  observed.  The  jackets  gg  serve  to  keep 
the  bars  at  any  desired  temperatures.  One  side  of  the  instru- 
ment, as  aa,  being  kept  at  a  constant  temperature,  a  change 
in  the  temperature  of  a' a'  will  cause  the  fringes  to  move, 
and  from  this  motion  of  the  fringes  the  change  in  length, 
which  is  caused  by  the  change  in  temperature,  can  be  very 
accurately  determined.  Fig.  51  shows  a  perspective  view  of 
the  apparatus. 

Evidently  the  same  kind  of  instrument  is  suitable  for 
experiments  in  elasticity,  and  one  of  these  was  shown  in  the 
last  lecture,  where  a  steel  axle  was  twisted  [cf.  Figs.  36  and 

1  MoELEY  AND  RoGEES,  Physical  Revieiv,  Vol.  IV  (1896),  pp.  1, 106. 


FIG.  50 


56 


Light  Waves  and  Theie  Uses 


37,  p.  39).  If  we  measure  the  couple  producing  the  twist, 
and  the  number  of  fringes  which  pass  by,  we  can  find  the 
corresponding  angle  of  twist,  and  a  simple  calculation  gives 
us  the  measure  of  our  coefficient  of  rigidity. 

The  interferometer  in   this  second  form  has  also  been 

applied  to  the 
balance.  Fig. 
52  shows  such 
an  arrangement. 
The  mirrors  of 
the  interferom- 
eter are  on  the 
upright  metal 
plate,  the  two 
movable  mirrors 
being  fastened 
to  the  ends  of 
the  arms  of  a 
balance  which 
is  just  visible 
within  the  horizontal  box.  The  object  of  this  particular 
experiment  was  to  determine  the  constant  of  gravitation; 
in  other  words,  to  find  the  amount  of  attraction  which  a 
sphere  of  lead  exerted  on  a  small  sphere  hung  on  an  arm  of 
the  balance.  The  amount  of  this  attraction,  when  the  two 
spheres  are  as  close  together  as  possible,  is  proportional  to 
the  diameter  of  the  large  sphere,  which  was  something  like 
eigrht  inches.  The  attraction  on  the  small  ball  on  the  end 
of  the  balance  was  thus  the  same  fraction  of  its  weight  as 
the  diameter  of  the  large  ball  was  of  the  diameter  of  the 
earth,  /'.  c,  something  like  one  twenty-millionth.'  So  the 
force  to  be  measured  was  one  twenty-millionth  of  the  weight 


FIG.  51 


I  This   ratio  takes  into  account  the  increased  attraction  duo  to  the  greater 
density  of  the  lead  sphere. 


Application  of  Inteeference  Methods       57 


of  this  small  ball.  This  force  is  so  exceedingly  small  that 
it  is  difficult  to  measure  it  by  an  ordinary  balance,  even 
if  the  microscope  is  employed.  But  by  the  interference 
method  the  approach  of  the  large  ball  to  the  small  one  pro- 
duced a  displacement  of  seven  whole  fringes.  The  number 
of  fringes  can  be  deter- 
mined to  something  of  the 
order  of  one-twentieth  of 
the  width  of  one  fringe. 
We  therefore  have  with 
this  instrument  the  means 
of  measuring  the  gravita- 
tion constant,  and  thence 
the  mass  of  the  whole  earth, 
to  within  about  y^y-  of  the 
whole.  By  still  more  sen- 
sitive adjustment  it  would 
be  possible  to  exceed  this 
degree  of  accuracy. 

An  instrument  in  which 
the  interferometer  is  used 
for  testing  the  accuracy  of 
a  screw  is  shown  in  Fig, 
53.  The  screw  which  was 
to  be  tested  by  this  device  was  intended  to  be  used  in  a 
ruling  engine  for  the  manufacture  of  diffraction  gratings. 
Now,  it  is  necessary,  in  ruling  gratings,  to  make  the  dis- 
tance between  the  lines  the  same  to  within  a  small  frac- 
tion of  a  micron.  The  error  in  the  position  of  any  of  the 
lines  must  be  less  than  a  ten-millionth  part  of  an  inch. 
Ordinarily  a  screw  from  the  best  machinists  has  errors  a 
thousand  times  as  great.  The  screw  must  then  be  tested 
and  corrected.  The  testing  is  often  done  with  the  micro- 
scope, but  here  the  microscope  is  replaced  by    the    inter- 


FIG. 


58 


Light  Waves  and  Theie  Uses 


ferometer,  with  a  corresponding  increase  in  the  delicacy  of 
the  test. 

I  will  conclude  by  showing  how  to  measure  the  length  of 
light  waves  by  means   of  the  interferometer.      By  turning 


FIG.  53 

the  head  attached  to  the  screw,  one  of  the  interferometer 
mirrors  (namely  C,  Fig.  39)  can  be  moved  very  slowly. 
This  motion  will  produce  a  corresponding  displacement  of 
the  interference  fringes.  Count  the  number  of  interference 
fringes  which  pass  a  fixed  point  while  the  mirror  moves  a 
given  distance.  Then  divide  double  the  distance  by  the 
number  of  fringes  which  have  passed,  and  we  have  the 
length  of  the  wave.  Using  a  scale  marked  from  0  to  10, 
made  of  such  a  size  and  placed  at  such  a  distance  that,  when 
a  beam  of  light  reflected  from  a  mirror  attached  to  the 
screw  moves  ovav  one  division,  a  difference  in  path  of  one- 


Application  of  Inteefekence  Methods      59 

thousandth  of  a  millimeter  has  been  introduced,  and  project- 
ing the  interference  fringes  upon  the  screen,  it  will  be  noted 
that  while  ten  or  twelve  of  these  fringes  move  past  the  fiducial 
line  the  spot  of  light  will  move  over  a  corresponding  dis- 
tance on  the  scale.  In  moving  through  ten  fringes  the  spot 
of  light  moves  through  six  of  the  divisions,  and  therefore 
the  length  of  one  wave  would  bo  six-tenths  of  a  micron, 
which  is  very  nearly  the  wave  length  of  yellow  light.  If  the 
light  passes  through  a  piece  of  red  glass,  and  the  experiment 
is  repeated,  the  wave  length  will  be  greater;  it  is  nearly 
sixty-seven  hundredths.  It  is  easy  to  see  how  the  process 
may  be  extended  so  as  to  obtain  very  accurate  measurements 
of  the  length  of  the  light  wave. 

SUMMAEY 

1.  A  comparison  between  the  corpuscular  and  the  undula- 
tory  theories  of  light  shows  that  the  speed  of  light  in  a 
medium  like  water  must  be  greater  than  in  air  according  to 
the  former,  and  less  according  to  the  latter.  In  spite  of  the 
inconceivable  swiftness  with  which  light  is  propagated,  it 
has  been  possible  to  prove  experimentally  that  the  speed  is 
less  in  water  than  in  air,  and  thus  the  corpuscular  theory  is 
proved  erroneous. 

2.  A  number  of  applications  of  the  interferometer  are 
considered,  namely,  (a)  the  measurement  of  the  index  of 
refraction ;  (6)  the  coefficient  of  expansion ;  (c)  the  coefficient 
of  elasticity;  (d)  the  thickness  of  the  "black  spot;"  (c)  the 
application  to  the  balance ;  (/)  the  testing  of  precision  screws; 
ig)  the  measurement  of  the  length  of  light  waves. 


LECTURE  IV 

THE   APPLICATION   OF   INTERFERENCE   METHODS  TO 
SPECTROSCOPY 

Doubtless  most  of  us,  at  some  time  or  other,  have  looked 
through  an  old-fashioned  prismatic  chandelier  pendant  and 
observed  that  when  held  horizontally  it  produces  the  very 
curious  effect  of  making  objects  appear  to  slope  downward 
as  though  going  down  hill;  and  certainly  you  have  all 
noticed  the  colored  border  which  such  a  pendant  produces 
at  the  edge  of  luminous  objects.  This  experiment  was  made 
first  under  proper  conditions  by  Newton,  who  allowed  a 
small  beam  of  sunlight  to  pass  through  a  narrow  aperture 
into  a  dark  room  and  then  through  a  glass  prism.  He 
observed  that  the  sun's  image  was  drawn  out  into  what  we 
call  a  spectrum,  i.  e.,  into  a  band  of  colors  which  succeed 
one  another  in  the  well-known  sequence  —  red,  orange,  yel- 
low, green,  blue, Violet;  the  red  being  least  refracted  and 
the  violet  most. 

If  Newton  had  made  his  aperture  sufficiently  narrow 
and,  in  addition,  had  introduced  a  lens  in  such  a  way 
that  a  distinct  image  of  the  slit  through  which  the  sun- 
light passed  was  formed  on  the  opposite  wall,  he  would 
have  found  that  the  spectrum  of  the  sun  was  crossed  by  a 
number  of  very  fine  lines  at  right  angles  to  the  direction  in 
which  the  colors  extended.  These  lines,  called  after  the  dis- 
coverer Fraunhofer's  lines,  have  this  very  important  char- 
acteristic, that  they  always  appear  at  certain  definite  positions 
in  the  spectrum ;  and  hence  they  were  used  for  a  considerable 
time  for  describing  the  location  of  the  different  colors  of 
the  spectrum.      We  shall  endeavor  roughly  to  present  this 

60 


Interference  Methods  in  Spectroscopy     G1 

experiment.  Not  having  sunlight,  however,  we  shall  take  an 
electric  arc  and  produce  a  spectrum.  It  will  be  noticed  that 
this  spectrum  is  not  crossed  by  black  lines,  but  that  it  is, 
at  least  for  our  purpose,  practically  continuous,  as  shown  on 
Plate  III,  No.  1.  Instead  of  using  the  electric  light,  let  us 
try  a  source  which  emits  but  a  single  color.  For  this  pur- 
pose we  shall  introduce  into  the  electric  arc  a  piece  of 
sodium  glass.  Instead  of  a  spectrum  of  many  colors,  we 
have  one  consisting  mainly  of  one  color,  namely,  of  one 
yellow  band.  This  yellow  band  in  reality  consists  of  two 
images  of  the  slit,  which  are  very  close  together,  as  can  be 
shown  by  making  the  slit  narrower,  for  then  the  two  lines 
will  also  become  narrower  in  proportion.  If,  instead  of 
sodium  glass,  we  introduce  a  rod  of  zinc,  then,  instead  of 
one  bright  yellow  line,  the  spectrum  consists  of  lines  in  the 
red,  green,  and  violet  —  two  or  three  in  the  violet,  one  in 
the  green,  and  one  in  the  red.  If  we  were  to  introduce 
copper,  the  spectrum  would  consist  of  quite  a  number  of  lines 
in  the  green;  and  if  other  substances  were  used,  other  lines 
would  appear  in  the  spectrum  (c/.  Plate  III,  Nos.  3  and  4). 
Now,  the  lines  produced  by  any  one  substance  are  found  to 
occur  always  at  a  particular  place  in  the  spectrum,  and  are 
thus  characteristic  of  the  substance  which  produces  them.  If, 
instead  of  the  electric  light,  we  had  used  sunlight,  we  should 
find,  as  Fraunhofer  did,  that  the  spectrum  of  the  sun  is  crossed 
by  a  number  of  fine,  dark  lines,  perhaps  as  many  as  one 
hundred  thousand,  distributed  throughout  the  spectrum. 
Some  of  the  more  important  of  these  lines  are  shown  in  Fig. 
54.  The  red  end  of  the  spectrum  is  at  the  bottom.  Only  the 
visible  portion  of  the  spectrum  of  the  sun  is  shown  in  the 
figure.  The  pair  of  dark  lines  marked  D  coincide  in  position 
with  the  bright  lines  which  are  produced  by  sodium,  as 
shown  on  Plate  III,  Nos.  2  and  3,  and  is  an  indication  of  the 
presence  of  sodium  in  the  sun's  atmosphere. 


62 


Light  Waves  and  Their  Uses 


FKJ.  51 


As  was  remarked  above,  this  sodium  line  is 
double,  i.  e.,  is  really  made  up  of  two  lines  close 
together.  The  distance  between  these  two  lines  is 
a  convenient  standard  of  measurement  for  our  sub- 
sequent work.  This  distance  is  so  small  that  a 
single  prism  scarcely  shows  that  the  line  is  double. 
As  we  increase  the  number  of  prisms,  the  lines  are 
separated  more  and  more  widely.  If,  instead  of  a 
prism,  we  use  one  of  the  best  grating  spectroscopes, 
the  two  lines  are  separated  so  far  that  we  might 
count  sixty  or  eighty  lines  between ;  and  this  fact 
gives  a  fair  idea  of  the  resolving  power  of  these 
instruments.  If  we  have  two  lines  so  close  to- 
gether as  to  be  separated  by  only  one-hundredth 
of  the  distance  between  these  two  sodium  lines, 
the  best  spectroscope  will  hardly  be  able  to  sepa- 
rate them;  i.  e.,  its  limit  of  resolution  has  been 
reached. 

The  difference  in  the  character  of  the  lines 
from  difPerent  substances  is  illustrated  in  Fig.  55. 
The  spectrum  that  you  have  just  seen  is  a  photo- 
graph from  a  drawing,  not  a  photograph  from  a 
spectrum.  These  are  from  spectra.  On  the  right 
is  a  portion  of  the  spectrum  of  iron,  the  other  the 
corresponding  portion  of  that  of  zinc.  The  enor- 
mous diversity  in  the  appearance  of  the  lines  will 
be  noted.  Some  are  exceedingly  fine — so  fine  that 
they  are  not  visible  at  all ;  others  are  so  broad  that 
they  cover  ten  or  twenty  times  the  distance  between 
two  sodium  lines.  This  width  of  the  lines  de- 
pends somewhat  upon  the  conditions  under  which 
the  different  substances  are  burned.  If  the  incan- 
descent vapor  which  sends  out  the  lines  is  very 
dense,  then  the  lines  are  very  In-oad ;  if  it  is  very 


Inteefeeence  Methods  in  Specteoscopy     63 


rare,  then  the  lines  are  exceedingly  narrow. 
Some  of  the  lines  are  double,  some  triple, 
and  some  are  very  complex  in  their  charac- 
ter; and  it  is  this  complexity  of  character  or 
structure  to  which  I  wish  particularly  to 
draw  your  attention. 

This  complexity  of  the  character  of  the 
lines  indicates  a  corresponding  complexity 
in  the  molecules  whose  vibrations  cause  the 
light  which  produces  these  lines;  hence  the 
very  considerable  interest  in  studying  the 
structure  of  the  lines  themselves.  In  very 
many  cases  —  indeed,  I  may  say,  in  most 
cases — this  structure  is  so  tine  that  even 
with  the  most  powerful  spectroscope  it  is 
impossible  to  see  it  all.  If  this  order  of  com- 
plexity, or  order  of  fineness,  or  closeness  of 
the  component  lines  is  something  like  one- 
hundredth  of  the  distance  we  have  adopted 
as  our  standard,  it  is  practically  just  beyond 
the  range  of  the  best  spectroscopes.  It 
therefore  becomes  interesting  to  attempt  to 
discover  the  structure  by  means  of  inter- 
ference methods. 

In  order  to  understand  how  interference 
can  be  made  use  of,  let  us  consider  the  nature 
of  the  interference  phenomena  which  would 
be  produced  by  an  absolutely  homogeneous 
train  of  waves,  /.  e.,  one  which  consisted  of 
only  one  definite  simple  harmonic  vibra- 
tion. If  such  a  train  of  waves  were  sent  into 
an  interferometer,  it  would  produce  a  definite 
set  of  fringes,  and  if  the  mirror  C  (Fig.  39) 
of  the  interferometer  were  moved  so  as  to 


FIG.  55 


64  Light  Waves  and  Theik  Uses 

increase  the  difference  in  path  between  the  two  interfering 
beams,  then,  as  was  explained  above  on  p.  58,  these  inter- 
ference fringes  would  move  across  the  field  of  view.  Now, 
in  this  case,  since  the  light  which  we  are  using  consists 
of  waves  of  a  single  period  only,  there  will  be  but  one  set  of 
fringes  formed,  and  consequently  the  difference  of  path  be- 
tween the  two  interfering  beams  can  be  increased  indefinitely 
without  destroying  the  ability  of  the  beams  to  produce  inter- 
ference. It  is  perhaps  needless  to  say  that  this  ideal  case 
of  homogeneous  waves  is  never  practically  realized  in 
nature. 

What  will  be  the  effect  on  the  interference  phenomena  if 
our  source  of  light  sends  out  two  homogeneous  trains  of 
waves  of  slightly  different  periods?  It  is  evident  that  each 
train  will  independently  produce  its  own  set  of  interference 
fringes.  These  two  sets  of  fringes  will  coincide  with  each 
other  when  the  difference  in  the  lengths  of  the  two  optical 
paths  in  the  interferometer  is  zero.  When,  however,  this 
difference  in  path  is  increased,  the  two  sets  of  fringes  move 
across  the  field  of  view  with  different  velocities,  because  they 
are  due  to  waves  of  different  periods.  Hence,  one  set  must 
sooner  or  later  overtake  the  other  by  one-half  a  fringe,  i.  e., 
the  two  systems  must  come  to  overlap  in  such  a  way  that  a 
bright  band  of  one  coincides  with  a  dark  band  of  the  other. 
When  this  occurs  the  interference  fringes  disappear.  It  is 
further  evident  that  the  difference  of  path  which  must  be 
introduced  to  bring  about  this  result  depends  entirely  on 
the  difference  in  the  periods  of  the  two  trains  of  waves,  i.  e., 
on  the  difference  in  the  wave  lengths,  and  that  this  disap- 
pearance of  the  fringes  takes  place  when  the  difference  of 
path  contains  half  a  wave  more  of  the  shorter  waves  than  of 
the  longer.  Hence  we  see  that  it  is  possible  to  determine 
the  difference  in  the  lengths  of  two  waves  by  observing  the 
distance    through    which  the  mirror  C  must   be   moved  in 


Interference  Methods  in  Spectroscopy    65 

passing  from  one  position  in  which  the  fringes  disappear  to 
the  next. 

If  the  two  homogeneous  trains  of  waves  have  the  same 
intensity,  then  the  two  sets  of  fringes  will  be  of  the  same 
brightness,  and  when  the  bright  fringe  of  one  falls  on  the 
dark  fringe  of  the  other,  the  fringes  disappear  entirely.  If, 
however,  the  two  trains  have  different  intensities,  one  set  of 
fringes  will  be  brighter  than  the  other,  and  the  fringes  will 
not  entirely  disappear  when  one  set  has  gained  half  a  fringe 
on  the  other.  In  this  case  the  fringes  will  merely  pass 
through  a  minimum  of  distinctness.  We  see  then  that,  if 
our  source  of  light  is  double,  i.  e.,  sends  out  light  of  two 
different  wave  lengths,  we  should  expect  to  see  the  clearness 
or  visibility  of  the  fringes  vary  as  the  difference  of  path 
between  the  two  interfering  beams  was  increased. 

If  we  invert  this  process  and  observe  the  interference 
fringes  as  the  difference  in  path  is  increased,  and  find  this 
variation  in  the  clearness  or  visibility  of  the  fringes,  it  is 
proved  with  absolute  certainty  that  we  are  dealing  with  a 
double  line.  This  is  found  to  be  the  case  with  sodium 
light,  and,  therefore,  by  measuring  the  distance  between  the 
positions  of  the  mirror  at  which  the  fringes  disappear,  we 
find  that  we  actually  can  determine  accurately  the  difference 
between  the  wave  lengths  of  the  two  sodium  lines.  In 
order  to  carry  the  analysis  a  step  farther,  suppose  that 
we  magnify  one  of  these  two  sodium  lines.  It  would 
probably  appear  somewhat  like  a  broad,  hazy  band.  For  the 
sake  of  simplicity,  however,  we  will  suppose  that  it  looks  like 
a  broad  ribbon  of  light  with  sharp  edges.  The  distance 
between  these  edges,  i.  e.,  the  width  of  this  one  line,  if  the 
sodium  vapor  in  the  flame  is  not  too  dense,  is  something 
like  one-fiftieth,  or,  perhaps,  in  some  _  cases  as  small  as 
one-hundredth,  of  the  unit  we  have  adopted  —  the  distance 
between  the  sodium  lines. 


66  Light  Waves  and  Their  Uses 

This  is  proved  by  noting  the  greatest  difference  in  path 
which  can  be  introduced  before  the  fringes  disappear  entirely. 
This  distance  is  different  for  different  substances,  and  the 
greater  it  is  the  narrower  the  line,  /.  c,  the  more  nearly  does 
it  approach  the  ideal  case  of  a  source  which  emits  waves  of 
one  period  only.  Now,  experiment  shows  that  the  fringes 
formed  by  one  sodium  line  will  overtake  those  formed  by  the 
other  in  a  distance  of  about  five  hundred  waves,  correspond- 
ing to  about  one-third  of  a  millimeter,  and  that  we  can 
observe  interference  fringes  with  sodium  light,  under  proper 
conditions,  until  the  difference  in  path  between  the  two 
interfering  beams  is  approximately  thirty  millimeters.  This 
means  that  the  width  of  the  band  is  something  like  one- 
hundredth  of  the  distance  between  the  two  bands.  The 
width  of  a  single  line  can  be  appreciated  in  the  ordinary 
spectroscope  when  the  sodium  vapor  is  dense,  and  under 
these  conditions  the  fringes  vanish  when  the  difference  in 
path  is  only  one-half  inch,  or  even  less.  When  we  try  to 
make  the  source  bright  by  increasing  the  temperature  and 
density  of  the  sodium  vapor  in  the  flame,  the  band  broadens 
out  to  such  an  extent  that  the  difference  in  path  over  which 
interference  can  be  observed  may  be  less  than  one-hundredth 
of  an  inch. 

The  above  discussion  of  the  case  of  the  two  sodium  lines 
may  easily  be  extended  to  include  lines  of  greater  complex- 
ity, and  it  will  be  found  that,  whatever  the  nature  of  the 
source,  the  clearness  or  visibility  of  the  fringes  will  vary  as 
the  difference  in  path  between  the  two  interfering  beams  is 
increased.  It  may  also  be  shown  that  each  particular  com- 
plex source  will  show  variations  in  the  visibility  of  the 
fringes  which  are  peculiar  to  it. 

Inversely  it  is  evident  that  by  the  observation  of  the 
character  of  the  curve  which  expresses  the  relation  between 
the  clearness  of  the  fringes  and  the  difference  of  path — the 


Interference  Methods  in  Spectroscopy     G7 


PIG.  56 


68  Light  Waves  and  Theie  Uses 

visibility  curve,  as  it  may  be  termed  —  we  can  draw  con- 
clusions as  to  the  character  of  the  radiations  which  cause  the 
interference  phenomena,  even  when  such  investigation  is 
beyond  the  power  of  the  best  spectroscopes.  In  order  to 
make  the  method  (it  may  perhaps  be  called  the  method  of 
light-wave  analysis)  an  accurate  process,  it  is  necessary,  in 
the  first  place,  to  produce  a  number  of  visibility  curves  from 
known  sources.  Thus,  for  example,  we  may  take  two  lines 
corresponding  to  the  sodium  lines,  and  produce  their  visibil- 
ity curve,  as  we  did  before,  by  adding  up  the  separate  fringes 
and  obtaining  the  resultant ;  we  may  then  take  three  or  four 
or  any  number  of  lines,  and  determine  the  corresponding 
visibility  curves.  Each  of  these,  instead  of  being  a  single 
line,  may  have  an  appreciable  breadth,  and  the  brightness 
of  the  line  may  be  distributed  in  various  ways  within  the 
breadth. 

Now,  the  process  of  adding  up  such  a  series  of  simple 
harmonic  curves  (for  the  interference  fringes  are  represented 
by  simple  harmonic  curves)  is  very  laborious.  Hence  the 
instrument  shown  in  Fig.  56,  called  a  harmonic  analyzer, 
was  devised  to  perform  this  work  mechanically.  It  looks 
very  complex  ;  in  reality  it  is  very  simple,  the  apparent 
complexity  arising  from  the  considerable  number  of  ele- 
ments required.  A  single  element  is  shown  in  Fig.  57. 
A  curved  lever  which  is  pivoted  at  o  is  represented  at  B. 
One  end  of  this  lever  is  attached  to  the  collar  of  the  eccen- 
tric A.  When  this  eccentric  revolves,  it  therefore  transmits 
to  the  lever  B  a  motion  which  is  very  nearly  simple  har- 
monic. The  amount  of  the  motion  which  is  communicated 
to  the  writing  lever  u  is  regulated  by  the  distance  of  the 
connecting  rod  B  from  the  axis  o.  When  the  connecting 
rod  is  on  one  side  of  the  axis  the  motion  is  positive;  when 
on  the  other  side  the  motion  would  be  negative.  The  end 
of  this  lever  is  connected  to  another  lever  x,  and  the  farther 


Interference  Methods  in  Spectroscopy      09 


FIG.  57 


70  Light  Waves  and  Their  Uses 

end  of  this  lever  is  connected  with  a  small  helical  spring  s. 
There  are  eighty  such  elements  arranged  in  a  row,  as  shown 
in  Fig.  56.  In  order  to  add  the  force  of  all  of  the  springs, 
they  are  connected  with  the  drum  C,  which  can  turn  about 
its  axis,  and  counterbalanced  by  a  very  much  larger  spring 
S  connected  to  the  other  side  of  the  drum.  This  gives  us 
the  means  of  adding  forces  which  are  proportional  to  the 
amount  of  displacement  of  the  lever  below,  and  hence  the 
sum  of  the  forces  of  these  eighty  springs  is  in  direct  propor- 
tion (at  any  rate  to  a  close  degree  of  approximation)  to  the 
sum  of  the  motions  themselves.  We  have  thus  a  mechanical 
device  for  adding  simple  harmonic  motions. 

To  illustrate  this  addition  of  simple  harmonic  motions 
by  means  of  our  machine,  one  of  the  connecting  rods  is  first 
moved  out  to  the  extreme  end  of  the  lever.  We  shall  then 
have  but  one  simple  harmonic  motion  to  deal  with,  and  this 
corresponds  to  an  absolutely  homogeneous  source.  The  re- 
sulting curve  is  the  first  one  in  Fig.  58.  Each  one  of  the 
oscillations  corresponds  to  an  interference  fringe,  and  there 
would  be  an  infinite  number  of  such  if  the  difference  in  path 
were  indefinitely  increased.  Now  we  will  take  the  case  of  two 
simple  harmonic  motions.  At  b,  curve  2,  the  fringes  have  dis- 
appeared completely.  One  series  of  fringes  has  just  overtaken 
the  other  by  one-half  a  fringe,  and,  therefore,  they  neutral- 
ize each  other.  At  c  the  fringes  have  begun  to  appear  again, 
and  at  d  they  have  attained  a  maximum  visibility  or  clear- 
ness. They  then  disappear  and  reappear  again,  and  so  on 
indefinitely. 

Curve  3  represents  the  case  of  the  two  sodium  lines,  each 
of  which  is  supposed  to  be  double.  It  will  be  observed  that 
in  this  case  there  are  two  periods ;  one,  the  same  as  that  of 
curve  2,  which  corresponds  to  the  double  sodium  line,  and 
the  other  a  longer  period  whose  first  minimum  occurs  at 
e  and  which  corresponds  to  the  shorter  distance  between  the 


Interfekence  Methods  in  Spectroscopy   71 

two  components  of  each  line.      The  conclusion  which  can  be 
drawn   from  observation  of  such  a  curve  as  this  is  that  the 


mmimmim!mimmm!mim!\im^ 


± 

Ai 


M^-«    M|\f^^^ — - — M/V\AAAM^^vA(\|\||' 


lll^^ 


FIG.  58 


source  which  was  used  in  obtaining  it  was  a  double  line,  each 
of  whose  components  was  double. 

Curve  4  represents  the  visibility  curve  of  two  lines,  one 
of  which  is  very  much  brighter  than  the  other,  but  whose 


72  Light  Waves  and  Their  Uses 

distance  apart  is  the  same  as  that  of  the  lines  of  curve  2. 
The  period  of  the  visibility  curve  is  the  same  as  that  of  2, 
but  instead  of  going  to  zero  it  merely  goes  to  a  minimum  at 
/.  Inversely,  when  we  get  such  a  curve  as  this  we  know  that 
one  of  the  lines  is  brighter  than  the  other — just  how  much 
brighter  can  be  learned  from  the  ratio  of  the  maximum  and 
minimum  ordinates. 

Curve  5  is  that  due  to  a  single  broad  source  of  uniform 
intensity  throughout.  It  will  be  noted  how  quickly  the 
fringes  lose  their  distinctness.  Curve  6  is  that  due  to  a  broad 
source  which  is  brighter  in  the  middle  than  at  the  edges. 
The  distribution  in  this  case  is  supposed  to  follow  the  expo- 
nential law.  The  corresponding  visibility  curve  does  not 
exhibit  maxima  and  minima,  but  gradually  dies  out  and 
remains  at  zero.  Curve  7  corresponds  to  a  double  source 
each  of  whose  components  is  brighter  in  the  middle.  Curve 
8  represents  a  triple  source  each  of  whose  components  is 
a  simple  harmonic  train  of  waves  of  the  same  intensity. 
Curve  9  represents  the  visibility  due  to  a  triple  source 
in  which  the  outer  components  are  much  fainter  than  the 
middle  one. 

We  might  go  on  indefinitely  constructing  on  the  machine 
the  visibility  curves  which  correspond  to  any  assumed  dis- 
tribution of  the  light  in  the  source.  The  curves  presented 
will  suffice  to  make  clear  the  fact  that  there  is  a  close 
connection  between  the  distribution  of  light  in  any  source 
and  the  visibility  curve  which  can  be  obtained  with  the 
use  of  that  source.  It  is,  however,  the  inverse  problem, 
i.  e.,  that  of  determining  the  nature  of  the  source  from 
observation  of  the  visibility  curve,  in  which  the  greatest 
interest  lies. 

In  order  to  determine  by  this  method  the  character  of 
the  source  with  which  we  are  dealing,  we  must  find  our  visi- 
bility curve  by  turning  the  micrometer  screw  of  the  inter- 


Interference  Methods  in  Spectroscopy  73 

ferometer  and  noting  the  clearness  of  the  fringes  as  the  dif- 
ference of  the  path  varies.  We  then  construct  a  curve 
which  shall  represent  this  variation  of  visibility  on  a  more 
or  less  arbitrary  scale,  and  compare  it  with  one  of  the  known 
forms,  such  as  those  shown  in  Pig.  58.  There  is,  however, 
a  more  direct  process.  The  explana- 
tion of  this  process  involves  so  much 
mathematics  that  I  shall  not  undertake 
it  here.  It  will  be  sufficient  to  state 
that  the  harmonic  analyzer  cannot  only 
be  used  as  has  been  described,  but  is 
also  capable  of  analyzing  such  visibility  ^^^-  ^^ 

curves.  Thus,  if  we  introduce  into  the  instrument  the  curve 
corresponding  to  the  visibility  curve,  by  making  the  distances 
of  the  connecting  rods  from  the  axis  proportional  to  the  ordi- 
nates  of  the  visibility  curve,  and  then  turn  the  machine,  it 
produces  directly  a  very  close  approximation  to  the  char- 
acter of  the  source.  For  example,  take  curve  2  of  Fig. 
58.  By  its  derivation  we  know  that  it  corresponds  to  a 
double  source  each  of  whose  components  is  absolutely  homo- 
geneous. If  we  introduce  this  curve,  or  rather  the  envelope 
of  it,  into  the  machine,  it  will  give  a  resultant  which  repre- 
sents the  character  of  the  source  to  a  close  degree  of  approxi- 
mation. The  actual  result  is  shown  in  Fig.  59,  in  which  the 
ordinates  represent  the  intensity  of  the  light.  We  thus  see 
that  the  machine  can  operate  in  both  ways,  L  e.,  that  it  can 
add  up  a  series  of  simple  harmonic  curves  and  give  the 
resultant,  which  in  the  case  before  us  is  the  visibility  curve, 
and  that  it  can  take  the  resultant  curve  and  analyze  it  into 
its  components,  which  here  represent  the  distribution  of  the 
light  in  the  source. 

Now  the  question  naturally  arises  as  to  how  the  observa- 
tions by  which  the  visibility  curve  is  determined  are  con- 
ducted;  also  as  to  what    units    to    adopt,  and    what    scale 


74  Light  Waves  and  Theie  Uses 


of  measurement.  It  is  apparently  something  very  indefi- 
nite. The  visibility  is  not  a  quantity  that  can  be  measured, 
as  we  can  a  distance  or  an  angle — unless,  to  be  sure,  we 
first  define  it.  After  defining  it  properly,  we  can  pro- 
duce, in  accordance  with  that  definition,  interference  fringes 
that  shall  have  any  desired  visibility.  By  the  use  of  fringes 
which  have  a  known  visibility  we  can  educate  the  eye  in 
estimating  visibility,  or  we  may  have  these  standard  fringes 
before  us  for  comparison  at  the  time  of  observation,  and 
may  then  determine  when  the  two  systems  are  of  the  same 
clearness;  and  when  they  are  of  the  same  clearness,  we  say 
that  the  desired  visibility  is  the  same  as  that  whose  value  is 
known  from  our  formula.  This  is  the  more  accurate  method, 
and  is  the  one  which  was  finally  adopted ;  but  long  before  its 
adoption  it  was  found  that  fairly  accurate  visibility  curves 
could  be  obtained  by  merely  agreeing  to  call  the  visibility 
100  when  it  was  perfect,  75  when  good,  and  50  when  fair. 
Then  25  would  be  rather  poor,  10  would  be  bad,  and  at  zero 
the  fringes  would  vanish.  Of  course,  there  would  be  a 
greater  or  less  difference  in  what  we  should  agree  to  call 
good,  but  in  general  we  can  tell  where  the  fringes  were  half 
as  clear  as  their  perfect  value,  provided,  of  course,  we  had 
this  perfect  value  given,  etc. 

As  a  matter  of  fact,  however,  it  is  not  of  the  utmost 
importance  to  determine  the  visibility  with  great  accuracy. 
We  know  that  we  can  measure  a  minimum  or  a  maximum 
independently  of  any  scale,  and  these  points  are  the  really 
important  ones.  For  example,  a  curve  may  come  to  zero 
gradually  or  abruptly  — ■  in  both  cases  the  distance  between 
the  two  lines  which  produced  the  curve  would  be  exactly  the 
same.  The  two  pairs  might  differ  in  character  in  other 
ways,  but  the  distance  between  the  two  components  of  each 
pair  would  be  the  same.  So,  even  without  an  absolute  scale 
that  we  have  tested,  and  even  without  any  very  great  amount 


Inteeference  Methods  in  Spectroscopy      75 


FIG.  60 


of  experience  in  observation,  we  can  get  a  very  fair  visi- 
bility curve,  and  from  that  a  very  fair  conception  of  the 
nature  of  the  spectrum  of  the  particular  source  we  are  exam- 
ining, by  merely  determining  the  points  of  maximum  and 
minimum  clearness. 

Before  discussing  some  of  the  visi- 
bility curves  that  have  been  obtained, 
I  should  like  to  say  a  word  concerning 
the  source  of  light.  When  the  source 
is  under  ordinary  conditions,  /.  e., 
under  atmospheric  pressure,  the  mole- 
cules are  not  vibrating  freely,  and  dis- 
turbing causes  come  in  to  make  the 
oscillations  not  perfectly  homogeneous. 
Hence  the  light  from  such  a  source, 
instead  of  being  a  definite,  sharp  line,  is  a  more  or  less 
diffuse  band.  In  order  to  obtain  the  character  of  the  line 
under  the  extreme  conditions,  i.  e.,  under  as  small  pres- 
sure as  possible,  the  substance  must  be  placed  in  a  vacuum 
tube.  The  tube  is  then  connected  to  an  air  pump  and 
exhausted  until  the  pressure  in  it  is  reduced  to  a  few  thou- 
sandths of  an  atmosphere. 

When  the  exhaustion  has  become  sufficient  —  the  time 
depending  on  the  particular  degree  of  exhaustion  required 
by  the  substance  which  we  wish  to  examine  —  the  tube  is 
heated  to  drive  off  the  remaining  water  vapor,  sealed  up,  and 
is  then  ready  for  use.  The  residual  gas  is  made  luminous 
by  the  spark  from  an  induction  coil.  In  some  cases  the 
substance  is  sufficiently  volatile  to  show  the  spectrum  at 
ordinary  temperatures;  e.  g.,  that  of  mercury  appears  after 
slight  heating.  In  the  case  of  such  substances  as  cad- 
mium and  zinc  the  tube  is  placed  in  a  brass  box,  as  illus- 
trated in  Fig.  60,  and  heated  until  the  substance  is  volatilized, 
a  thermometer  giving  us  an  idea  of  the  temperature  reached. 


76 


Light  Waves  and  Theie  Uses 


Fig.  61  illustrates  the  arrangement  of  the  apparatus 
as  it  is  actually  used.  An  ordinary  prism  spectroscope 
gives  a  preliminary  analysis  of  the  light  from  the  source. 


'^ 


FIG.  61 


This  is  necessary  because  the  spectra  of  most  substances 
consist  of  numerous  lines.  For  example,  the  spectrum  of 
mercury  contains  two  yellow  lines,  a  very  brilliant  green 
line,  and  a  less  brilliant  violet  line.  If  we  pass  all  the 
light  together  into  the  interferometer,  we  have  a  combina- 
tion of  all  four.  It  is  usually  better  to  separate  the  various 
radiations  before  they  enter  the  interferometer.  Accord- 
ingly, the  light  from  the  vacuum  tube  at  a  passes  through  an 


Interference  Methods  in  Spectroscopy     77 

ordinary  spectroscope  bed,  and  the  light  from  only  one  of 
the  lines  in  the  spectrum  thus  formed  is  allowed  to  pass 
through  the  slit  d  into  the  interferometer. 

As  explained  above,  the  light  divides  at  the  plate  e,  part 
going  to  the  mirror/,  which  is  movable,  and  part  passing 
through  to  the  mirror  g.  The  first  ray  returns  on  the  path/e/i. 
The  second  returns  to  e,  is  reflected,  and  passes  into  the  tele- 
scope h.  If  the  two  paths  are  exactly  equal,  we  have  inter- 
ference phenomena  in  white  light;  but  for  monochromatic 
light  the  difference  of  path  (from  the  point  e  to  the  mirror  /, 
and  from  the  same  point  to  the  mirror  g)  may  be  very  consid- 
erable. Indeed,  in  some  cases  interference  can  be  obtained 
when  the  difference  in  the  two  paths  amounts  to  over  half  a 
million  waves. 

It  is  rather  important  to  note  that  the  surface  of  the 
mirror  g  must  be  so  set  by  means  of  the  adjusting  screws 
at  its  back  that  its  image  in  the  mirror  e  shall  be  parallel 
with  the  surface  of  the  movable  mirror/.  When  this  is 
the  case  the  fringes,  instead  of  being  straight  lines,  as  in 
the  case  of  the  fringes  in  white  light,  are  concentric  circles 
very  similar  in  appearance  to  Newton's  rings.  Having  thus 
adjusted  the  interferometer  so  that  the  fringes  are  circles,  the 
difference  in  path  is  increased  by  turning  the  micrometer 
screw  a  definite  amount,  say  half  a  millimeter  at  a  time.  At 
every  half  millimeter  an  observation  is  taken  of  the  visibility, 
and  then  these  readings  are  plotted  on  co-ordinate  paper  as 
ordinates,  the  corresponding  difference  of  path  serving  as 
abscissae.  The  ends  of  these  ordinates  trace  out  the  visi- 
bility curve.  This  curve  is  then  set  on  the  harmonic  ana- 
lyzer, as  described  above,  and  the  machine  turns  out  the  curve 
corresponding  to  the  distribution  of  the  light  in  the  line 
examined. 

In  this  way  the  radiations  of  many  substances  were 
analyzed,  and   in  almost  every  case   it  was  found  that  the 


78 


Light  Waves  and  Theie  Uses 


line  was  not  produced  by  homogeneous  vibrations,  but  was 
double,  treble,  or  even  more  complex.  The  distances 
between  the  components  of  these  compound  lines  are  so 
small  that  it  is  practically  impossible,  except  in  a  few  cases, 
to  observe  them  in  the  ordinary  spectroscope. 

The  following  diagrams  (Figs.  62-8)  present  a  number 
of  these  visibility  curves.  Thus  Fig.  62  represents  that 
obtained  from  the  red  radiation  of  hydrogen.  The  curve 
to  the  right  represents  the  visibility  curve,  while  on  the 
left  the  corresponding  distribution  of  the  light  is  drawn. 
Beginning  at  a  difference   of  path  zero,    the  visibility  was 


FIG.  62 


100,  and  at  one  millimeter  it  was  somewhat  less,  and  so  on, 
until  at  about  seventeen  millimeters  we  find  a  minimum. 
As  the  difference  in  path  increases,  we  find  that  there  is  a 
maximum  at  twenty-three  millimeters.  After  that  the  curve 
slopes  down,  and  at  about  thirty-five  millimeters  it  disappears 
entirely.  Since  the  curve  is  periodic,  we  may  be  pretty  sure 
that  this  red  line  of  hydrogen  is  a  double  line.  This  fact,  I 
believe,  has  never  yet  been  observed,  though  the  distance 
between  the  two  components  is  not  beyond  the  range  of  a 
good  spectroscope,  being  about  one-fortieth  or  one-fiftieth 
of  the  distance  between  sodium  lines.' 

Fig.  63  represents  the  curve  which  was  obtained  from 
sodium  vapor  in  a  vacuum  tube.  When  we  burn  sodium  at 
atmospheric  pressure — as,  for  example,  when  we  place  sodium 

1  This  prediction  has  since  been  amply  confirmed  by  direct  observation. 


Inteefeeenoe  Methods  in  Speoteoscopy     79 

glass  in  a  Bunsen  flame  —  the  visibility  curve  due  to  its  radi- 
ations diminishes  so  rapidly  that  it  reaches  zero  when  the 
difference  of  path  is  about  forty  millimeters ;  it  is  practically 


FIG.  63 

impossible  to  go  farther  than  this.  It  is  seen  that  the  curve 
is  periodic,  which  would  indicate  that  each  one  of  the 
sodium  lines  is  a  double  line.  The  intensity  curve  at  the 
left  represents  one  of  the  sodium  lines  only.  The  other,  on 
the  same  scale,  would  be  distant  about  half  a  meter.  We 
can  from  this  get  some  idea  of  the  relative  sensitiveness  of 
this  process  of  light-wave  analysis,  as  compared  with  that  of 
ordinary  spectrum  analysis.  It  will  be  observed  that  the 
intensity  curve  shows  still  another  small  component  which 
corresponds  to  still  another  longer  period,  but  the  existence 
of  these  short  companion  lines  is  not  absolutely  certain. 


FIG.  64 


Fig.  64  represents  the  curve  of  thallium.  The  oscilla- 
tion shows  that  it  is  a  double  line,  and  not  very  close.  The 
distance  between  the  components  is  about  one-sixtieth  of  the 
distance  between  the  sodium  lines.  We  have  also  a  longer 
oscillation  which  shows  that  each  one  of  the  components  is 


80 


Light  Waves  and  Theik  Uses 


double.  The  distance  between  these  small  components  and 
the  larger  ones  is  something  like  one-thousandth  of  the  dis- 
tance between  sodium  lines,  corresponding  to  a  separation 
of  lines  far  beyond  the  possible  limit  of  the  most  powerful 
spectroscope. 

The  curve  of  the  green  radiation  of  mercury  is  shown  in 
Fig.  65.  This  curve  is  really  so  complicated  that  the  char- 
acter of  the  source  is  still  a  little  in  doubt.  The  machine  has 
not  quite  enough  elements  to  resolve  it  satisfactorily,  having 
but  eighty  when  it  ought  to  have  eight  hundred.     The  curve 


FIG.  65 


looks  almost  as  though  it  were  the  exceptional  result  of  this 
particular  series  of  measurements,  and  we  might  imagine  that 
another  series  of  measurements  would  give  quite  a  different 
curve.  But  I  have  actually  made  over  one  hundred  such 
measurements,  and  each  time  obtained  practically  the  same 
results,  even  to  the  minutest  details  of  secondary  waves. 
The  nearest  interpretation  I  can  make  as  to  the  character 
of  the  spectral  source  is  given  at  the  left  of  this  diagram. 
It  will  be  noticed  that  the  width  of  the  whole  structure 
is,  roughly  speaking,  one-sixtieth  of  the  distance  between 
the  sodium  lines.  The  distance  between  the  close  compo- 
nents of  the  brighter  line  is  of  the  order  of  one-thousandth 
of  the  distance  between  the  sodium  lines.  The  fringes 
in  this  case  remain  visible  up  to  a  difference  of  path  of 
400  millimeters,  and  they  have  actually  been  observed 
up  to  480  millimeters,  or  nearly  one-half  meter's  differ- 
ence in  path  —  corresponding  to  something  like  780,000 
waves. 


Inteefeeence  Methods  in  Specteoscopy     81 

In  the  curve  of  Fig.  66  we  have  quite  a  contrast  to  the 
preceding.  Here  we  have  a  radiation  almost  ideally  homo- 
geneous. Instead  of  having  numerous  maxima  and  minima 
like  the  curves  we  have  been  considering,  this  visibility  curve 
diminishes  very  gradually  according  to  a  very  simple  mathe- 
matical law,  which  tells  us  that  the  source  of  light  is  a 
single  line  of  extremely  small  breadth,  the  breadth  being  of 
the  order  of  one  eight-hundredth  to  one-thousandth  of  the 


FIG.  66 

distance  between  the  sodium  lines.  It  is  impossible  to 
indicate  exactly  the  width  of  the  line,  because  the  distribu- 
tion of  intensity  throughout  it  is  not  uniform.  The  impor- 
tant point  to  which  I  wish  to  call  attention,  however,  is  that 
this  curve  is  of  such  a  simple  character  that  for  a  difference 
of  path  of  over  200  millimeters,  or  400,000  light  waves, 
we  can  obtain  interference  fringes.  This  indicates  that  the 
waves  from  this  source  are  almost  perfectly  homogeneous. 
It  is  therefore  possible  to  use  these  light  waves  as  a  stand- 
ard of  length,  as  will  be  shown  in  a  subsequent  lecture. 
The  curve  corresponds  to  the  red  radiation  from  cadmium 
vapor  in  a  vacuum  tube.  In  using  this  red  cadmium  wave 
as  a  standard  of  length  it  is  very  important  to  have  other 
radiations  by  which  we  can  check  our  observations.  The 
cadmium  has  two  other  lines,  which  serve  as  a  control  or 
check  to  the  result  obtained  by  the  first. 

Fig.    67    represents    the    green    radiation    of    cadmium. 
This  curve  is  not  quite  so  simple  as  that  of  the  red,  but 


82 


Light  Waves  and  Theie  Uses 


extends  almost  to  200  millimeters.      The  corresponding  line 
is  shown  to  be  a  close  double. 

The  curve  corresponding  to  the  violet  light  of  cadmium 
is  shown  in  Fig.  68,  and  is  seen  to  be  comparatively  simple. 


Jl 


FIG.  67 


We  have  thus  shown  that  spectral  lines  are  complex  dis- 
tributions of  light,  whose  resolution  in  general  is  beyond  the 
power  of  the  spectroscope.  This  complexity  of  the  spectral 
lines  is  particularly  interesting  because  it  indicates  a  corre- 
sponding complexity  of  the  molecules  which  cause  the  vibra- 
tions which   give  rise   to   the   corresponding  spectral  lines. 


JL 


FIG.  G8 


This  complexity  may  be  likened  to  the  complexity  of  a  solar 
system ;  and  while  this  may  bring  dismay  to  the  Keplers  and 
Newtons  who  may  hope  to  unravel  the  mysteries  of  this  pigmy 
world,  it  certainly  increases  the  interest  in  the  problem. 


Intekference  Methods  in  Spectroscopy     S3 

SUMMARY 

1.  The  spectrum  of  the  light  emitted  by  incandescent 
gases  is  not  continuous,  but  is  made  up  of  a  number  of 
bright  lines  whose  position  in  the  spectrum  is  very  definite, 
and  which  are  characteristic  of  the  elements  which  produce 
them. 

2.  These  "lines"  are  not  such  in  a  mathematical  sense, 
but  have  an  appreciable  width  and  a  varying  distribution  of 
light,  and  in  some  cases  are  highly  complex. 

3.  This  variation  in  distribution  is,  however,  restricted  to 
such  narrow  limits  that  in  most  cases  it  is  impossible  to 
investigate  it  by  the  best  spectroscopes ;  but  by  the  method 
of  visibility  curves  the  lines  may  be  resolved  into  their 
elements. 

4.  An  important  auxiliary  for  the  interpretation  of  the 
visibility  curves  is  the  harmonic  analyzer — an  instrument 
which  sums  up  any  number  of  simple  harmonic  motions,  and 
which  also  analyzes  any  complex  motion  into  its  simple 
harmonic  elements. 


LECTURE  V 

LIGHT  WAVES  AS  STANDARDS   OF  LENGTH 

In  the  last  lecture  it  was  shown  that  in  many  cases  the 
interference  fringes  could  be  observed  with  a  very  large  dif- 
ference in  path — a  difference  amounting  to  over  500,000 
waves.  It  may  be  inferred  from  this  that  the  wave  length, 
during  the  transmission  of  500,000  or  more  waves,  has 
remained  constant  to  this  degree  of  accuracy;  that  is, 
the  waves  must  be  alike  to  within  one  part  in  500,000.  The 
idea  at  once  suggests  itself  to  use  this  invariable  wave 
length  as  a  standard  of  length.  The  proposition  to  make 
use  of  a  light  wave  for  this  purpose  is,  I  believe,  due  to  Dr. 
Gould,  who  mentioned  it  some  twenty-five  years  ago.  The 
method  proposed  by  him  was  to  measure  the  angle  of  dif- 
fraction for  some  particular  radiation  —  sodium  light,  for 
example  — with  a  diffraction  grating.  If  we  suppose  Fig.  69 
to  represent,  on  an  enormously  magnified  scale,  the  trace 
of  such  a  grating,  then  the  light  for  a  particular  wave 
length  —  say  one  of  the  sodium  lines —  which  passes  through 
one  of  the  openings  in  a  certain  direction,  as  AB,  is  re- 
tarded, over  that  which  passes  through  the  next  adjacent 
opening,  by  a  constant  difference  of  path;  and  therefore 
in  the  direction  AB  all  the  waves,  even  those  which  pass 
through  the  last  of  a  very  large  number  of  such  apertures, 
are  in  exactly  the  same  phase.  There  will  be  then,  if  we 
are  observing  in  a  spectrum  of  the  first  order,  as  many  waves 
in  this  distance  AB  as  there  are  apertures  in  the  distance 
AC.  A  diffraction  grating  is  made  by  ruling  upon  a  glass  or 
a  metal  surface  a  great  number  of  very  fine  lines  by  a  ruling 
diamond,  the  number  being  recorded  by  the  ruling-machine 

84 


Light  Waves  as  Standards  of  Length        85 

itself,  so  that  there  can  be  no  error  in  determining  the  number 

of  rulings.    This  number  is  usually  very  large,  between  50,000 

and  100,000.   Since  this  number  of  lines  is  accurately  known, 

we  know  also  the  number  of  spaces  in  the  whole  distance  AC. 

This  distance  can  be  measured  by  comparing  the  two  end 

rulings  with  an  intermediate 

A                                                  C 
standard   of    length,  which      x —  \ —  \ —  >, —  n  —  \ —  v— > 

has  been  compared  with  the       \    \    \     \      \     '^'m 

standard  yard  or  the  stand-  \     \     \     \  ^<^ 

1  \     \     \  .-^^ 

ard  meter    with   as  high   a  \      \J^ 

degree  of  accuracy  as  is  pos-  ^)^^^^^ 

sible  in  mechanical  measure- 

FIG.  69 

ments.      If,  now,  we    know 

also  the  angle  ACB,  we  can  calculate  the  distance  AB;  and 
since  we  know  the  number  of  waves  in  this  distance,  which 
is  the  same  as  the  number  of  apertures,  we  have  the  means 
of  measuring  the  length  of  one  wave.  It  will  be  observed, 
in  making  such  an  absolute  determination  of  wave  length  by 
this  means,  that  we  have  to  depend  entirely  upon  the  accu- 
racy of  the  distance  between  the  lines  on  the  grating — a 
distance  which  is  measured  by  a  screw  advancing  through  a 
small  proportion  of  its  circumference  for  each  line  ruled.  If 
the  intervals  between  the  lines  are  not  exactly  equal,  then 
there  will  be  an  error  introduced,  notwithstanding  every  pre- 
caution taken,  which  it  is  extremely  difficult,  if  not  impossible, 
to  correct. 

Another  error  may  be  introduced  in  making  the  com- 
parison of  the  two  extreme  lines  on  the  grating  with  the 
standard  decimeter.  This  error  may,  roughly,  be  said  to 
amount  to  something  like  one-half  a  micron,  i.  e.,  one-half 
of  one-thousandth  of  a  millimeter.  If,  then,  the  entire 
length  of  the  ruling  is  fifty  millimeters,  and  the  error,  say, 
one  ten-thousandth  of  a  millimeter,  the  wave  length  may  be 
measured  to  within  one  part  in  500,000.     This  is  the  error 


86  Light  Waves  and  Their  Uses 

upon  the  supposition  that  our  standard  is  absolutely  cor- 
rect. But  the  length  of  the  standard  decimeter  itself  has 
to  be  determined  by  means  of  microscopic  measurements,  and 
since  the  temperature  plays  a  considerable  role,  it  is  difficult 
to  avoid  errors  very  much  larger  than  those  due  to  the 
microscope.  If  we  combine  all  these  errors,  we  can  probably 
attain  at  best  an  accuracy  in  all  measurements  involved  of  the 
order  of  one  part  in  100,000.  Finally,  we  have  to  measure 
the  angle  ACB,  and  it  is  very  much  more  difficult  to 
measure  angles  than  lengths.  All  these  errors — the  measure- 
ment of  the  angle,  the  error  in  the  determination  of  the 
distance  AC,  that  in  the  comparison  of  the  intermediate 
standard  which  we  use,  and  that  in  the  distribution  of  these 
spaces — may  combine  in  such  a  way  that  the  total  error  may 
amount  to  very  much  more  than  one  part  in  100,000;  it 
may  be  one  in  20,000  or  30,000.  This  degree  of  accuracy, 
however,  is  greater  than  that  attained  by  either  of  the  other 
two  methods  which  have  been  proposed  for  establishing  an 
absolute  standard  of  length. 

The  first  of  these  proposed  standards  was  the  length  of 
the  pendulum  which  vibrates  seconds  at  Paris.  Such  a 
pendulum  may  be  obtained  by  suspending  from  a  knife 
edge  a  steel  rod  upon  which  a  large  lens-shaped  brass  bob 
is  fastened.  The  steel  rod  carries  another  knife  edge  near 
the  other  end,  so  that  the  pendulum  can  be  turned  over  so 
as  to  be  suspended  from  this  lower  knife  edge.  The  pen- 
dulum must  then  be  adjusted  so  that  its  time  of  vibration  is 
exactly  the  same  in  either  position,  which  can  be  done  with 
but  little  difficulty.  When  such  a  pendulum  vibrates  seconds 
in  either  position,  the  distance  between  the  knife  edges  is 
the  length  of  a  simple  seconds  pendulum. 

We  may  also  construct  a  simple  pendulum  by  fastening  a 
sphere  of  metal  to  the  end  of  a  thin,  fine  wire.  It  is  then 
necessary  to  measure  the  time  of  oscillation,  and  the  distance 


Light  Waves  as  Standards  of  Length        87 

between  the  point  of  suspension  and  the  center  of  gravity 
of  the  spherical  bob.  This  distance  can  be  measured  to  a 
very  fair  degree  of  accuracy.  Unfortunately  the  different 
observations  vary  among  themselves  by  quantities  even 
greater  than  the  errors  of  the  diffraction  method. 

The  second  of  these  proposed  standards  was  the  circum- 
ference of  the  earth  measured  along  a  meridian,  as  it  was 
believed  that  this  distance  is  probably  invariable.  There 
are,  however,  certain  variations  in  the  circumference  of  the 
earth,  for  we  know  that  the  earth  must  be  gradually  cool- 
ing and  contracting.  The  change  thus  produced  is  prob- 
ably exceedingly  small,  so  that  the  errors  in  measuring  this 
circumference  would  not  be  due  so  much  to  this  cause  as  to 
others  inherent  to  the  method  of  measuring  the  distance 
itself.  For  suppose  we  determine  the  latitude  of  two  places, 
one  4:5°  north  of  the  equator  and  one  45°  south.  The  dif- 
ference in  latitude  of  these  places  can  be  determined 
with  astronomical  precision.  The  distance  between  the 
places  is  one-fourth  of  the  entire  circumference  of  the 
earth.  This  distance  must  be  measured  by  a  system  of  tri- 
angulation  —  a  process  which  is  enormously  expensive  and 
requires  considerable  time  and  labor;  and  it  is  found  that 
the  results  of  these  measurements  vary  among  themselves 
by  a  quantity  even  greater  than  do  those  reached  with  the 
pendulum.  So  that  none  of  these  three  methods  is  capable 
of  furnishing  an  absolute  standard  of  length. 

While  it  was  intended  that  one  meter  should  be  the  one 
forty-millionth  of  the  earth's  circumference,  in  consequence 
of  these  variations  it  was  decided  that  the  standard  meter 
should  be  defined  as  the  arbitrary  distance  between  two 
lines  ruled  on  a  metal  bar  a  little  over  a  meter  long,  made 
of  an  alloy  of  platinum  and  irridium.  It  was  made  of 
these  two  substances  principally  on  account  of  hardness  and 
durability.      In  order  to  bring  the  metal  as  nearly  as  possible 


Light  Weaves  and  Their  Uses 


to  what  was  termed  its  "permanent  condition,"  these  bars 
were  subjected  to  all  sorts  of  treatment  and  maltreatment. 
The  originals  were  cast  and  recast  a  great  many  times,  and 
afterward  they  were  cooled  —  a  process  which  took  several 
months. 

After  such  treatment  it  is  believed  that  the  alteration  in 
length  of  these  bars  will  be  exceedingly  small,  if  anything 
at  all.  But,  as  a  matter  of  fact,  it  is  practically  impos- 
sible to  determine  such  small  alterations,  because,  while 
there  have  been  a  number  of  copies  made  from  this  funda- 
mental standard,  these  copies  are  all  made  of  the  same  metal 
as  the  original;  hence,  if  there  were  any  change  in  the 
original,  there  would  probably  be  similar  changes  in  all  the 
copies  simultaneously,  and  it  would  therefore  be  impossible 
to  detect  the  change.  The  extreme  variation,  however,  must 
be  of  the  order  of  one-thousandth  of  a  millimeter  or  less 
in  the  whole  distance  of  1,000  millimeters. 

The  question  rightly  arises  then:  Why  require  any  other 
standard,  since  this  is  known  to  be  so  accurate?  The 
answer  is  that  the  requirements  of  scientific  measurement 
are  growing  more  and  more  rigorous  every  year.  A 
hundred  years  ago  a  measurement  made  to  within  one- 
thousandth  of  an  inch  was  considered  rather  phenomenal. 
Now  it  is  one  of  the  modern  requirements  in  the  most 
accurate  machine  work.  At  present  a  few  measurements 
are  relied  upon  to  within  one  ten-thousandth  of  an  inch. 
There  are  cases  in  which  an  accuracy  of  one-millionth  of 
an  inch  has  been  attained,  and  it  is  even  possible  to 
detect  differences  of  one  five-millionth  of  an  inch.  Past 
experience  indicates  that  we  are  merely  anticipating  the 
requirements  of  the  not  too  distant  future  in  producing 
means  for  the  determination  of  such  small  quantities. 
Again,  in  order  that  the  results  of  scientific  work  already 
completed,  or  shortly  to  be  completed,  may  be  compared 


Light  Waves  as  Standards  of  Length        89 

and  checked  with  those  of  subsequent  researches,  it  is  essen- 
tial that  the  units  and  standards  employed  should  have  the 
same  meaning  then  as  now,  and,  therefore,  that  such  stand- 
ards should  be  capable  of  being  reproduced  with  the 
highest  attainable  order  of  accuracy.  We  may,  perhaps,  say 
that  the  limit  of  such  attainable  accuracy  is  the  accuracy 
with  which  two  of  the  standards  can  be  compared,  and 
this  is,  roughly  speaking,  about  one-half  of  a  micron  — 
some  say  as  small  as  three-tenths  of  a  micron.  For  such 
work  neither  of  the  three  methods  described  above  of  pro- 
ducing a  standard  is  sufficiently  accurate.  As  before  stated, 
the  results  obtained  by  them  vary  among  themselves  by 
quantities  of  the  order  of  one  part  in  50,000  to  one  part  in 
20,000.  Since  the  whole  meter  is  1,000,000  microns,  an 
order  of  accuracy  of  one-half  of  a  micron,  which  can  be 
obtained  with  a  microscope,  would  mean  one  part  in  2,000,- 
000,  which  is  far  beyond  the  possibilities  of  any  of  the  three 
methods  proposed. 

We  now  turn  to  the  interference  method.  Some  pre- 
liminary experiments  showed  that  there  were  possibilities  in 
this  method.  The  fact  to  which  we  have  just  drawn  atten- 
tion—  namely,  that  the  wave  lengths  are  the  same  to  at  least 
one  part  in  500,000 — looks  particularly  promising  and  leads 
us  to  believe  that,  if  we  had  the  proper  means  of  using  the 
waves  and  of  multiplying  them  up  to  moderately  long  dis- 
tances, without  multiplying  the  errors,  they  could  be  used 
as  a  standard  of  length  which  would  meet  the  requirement. 
This  requirement  is  that  a  sufficient  number  of  waves  shall 
produce  a  length  which  may  be  reproduced  with  such  a 
degree  of  accuracy  that  the  difference  between  the  new 
standard  and  the  one  now  serving  as  the  standard  cannot 
be  detected  by  the  microscope. 

The  process  is,  in  principle,  an  ideally  simple  one,  and 


90  Light  Waves  and  Theik  Uses 

consists  in  counting  the  number  of  waves  in  a  given  distance. 
However,  in  counting  such  an  enormous  number,  of  the 
order  of  several  hundred  thousands,  one  is  liable  to  make  a 
blunder  —  not  an  error  in  a  scientific  sense,  but  a  blunder. 
Of  course,  ultimately,  this  would  be  detected  by  the  process 
of  repetition. 

The  investigation,  in  a  concrete  form,  presents  a  number 
of  interesting  points,  involving  problems  of  construction  of 
a  unique  character  which  had  to  be  solved  before  the  process 
could  be  said  to  be  perfectly  successful. 

The  construction  and  operation  of  the  apparatus  will  be 
much  more  readily  understood  if  we  first  dwell  a  little  upon 
the  conditions  that  are  to  be  fulfilled.  Suppose,  for  illustra- 
tion, that  it  is  required  to  find  the  distance  between  two- 
mile  posts  on  a  railroad  track.  The  most  convenient  method 
for  measuring  such  a  distance  would  be  by  a  hundred- 
foot  steel  tape  stretched  by  a  known  stretching  force  and 
applied  to  the  steel  rails.  The  rails  are  mentioned  simply 
in  order  that  there  should  not  be  any  sag  of  the  tape  which 
would  introduce  still  another  error.  The  zero  mark  of  the 
tape  being  placed  against  a  mark  on  the  rail  which  serves 
as  the  starting-point,  a  second  mark  is  made  on  the  rail 
opposite  the  hundred-foot  mark  of  the  tape.  The  tape 
is  then  placed  in  position  a  second  time  with  one  end  on 
the  second  mark,  and  a  third  mark  is  placed  at  the  farther 
end;  and  so  on  indefinitely.  This  is  the  first  process.  By 
it  we  have  divided  the  mile  into  the  nearest  whole  number 
of  hundred-foot  spaces.      Then  we  measure  the  fractions. 

The  second  operation  consists  in  verifying  the  length  of 
the  steel  tape,  which  we  must  do  by  comparing  it  with  a 
standard  yard  or  foot  by  the  same  stepping-off  process. 

The  process  of  measuring  the  meter  in  light  waves  is 
essentially  the  same  as  that  described  above,  the  meter 
answering    to    the    distance    of    a    mile   of    track,    and    the 


Light  Waves  as  Standaeds  op  Length        91 

liundred-foot  tape  corresponding  to  a  considerably  smaller 
distance.  This  smaller  distance  is  what  I  have  termed  an 
"intermediate  standard."  There  is  in  this  latter  case  the 
additional  operation  of  finding  the  number  of  light  waves  in 
the  intermediate  standard ;  so  that,  in  reality,  there  are  three 
distinct  processes  to  be  considered. 

In  the  first  operation  it  is  evident  that,  if  an  error  is  com- 
mitted whenever  we  lift  the  tape  and  place  it  down  again, 
the  smaller  the  number  of  times  we  lift  it  and  place  it  down, 
the  smaller  the  total  error  produced ;  hence,  one  of  the  essen- 
tial conditions  of  our  apparatus  would  be  to  make  this  small 
standard  as  long  as  possible.  The  length  of  the  intermediate 
standard  is,  however,  limited  by  the  distance  at  which  we  can 
observe  interference  fringes.  The  limit,  as  was  stated  in  the 
last  lecture,  is  reached  when  this  distance  is  of  the  order  of 
several  hundred  thousand  waves.  At  this  distance  the  inter- 
ference fringes  are  rather  faint,  and  it  seemed  better  for 
such  determinations  not  to  make  use  of  the  extreme  distance, 
but  of  such  a  smaller  distance  as  would  insure  distinct  inter- 
ference fringes.  It  was  found  convenient  to  use,  as  the  max- 
imum length  of  the  intermediate  standard,  one  decimeter. 
The  number  of  light  waves  in  the  difference  of  path  (which 
is  twice  the  actual  distance,  because  the  light  is  reflected 
back)  would  be  something  of  the  order  of  three  or  four 
hundred  thousand  waves.  With  such  a  difference  of  path  we 
can  still  see  interference  fringes  comparatively  clearly,  if  we 
choose  the  radiating  substance  properly. 

The  investigrations  described  in  the  last  lecture  showed 
that  the  radiations  emitted  by  quite  a  number  of  the  sub- 
stances which  were  examined  were  more  or  less  highly  com- 
plex. One  remarkable  exception,  however,  was  found  in 
the  red  radiation  of  cadmium  vapor.  This  particular  radia- 
tion proved  to  be  almost  ideally  homogeneous,  i.  e.,  to  con- 


92  Light  Waves  and  Theie  Uses 

sist  very  nearly  of  a  series  of  simple  harmonic  vibrations. 
This  radiation  was  therefore  eminently  suited  to  the  purpose, 
and  was  adopted  as  the  standard  wave  length. 

Most  substances  produce  a  more  or  less  complicated  spec- 
trum involving  quite  a  number  of  lines,  but  in  the  case  of 
cadmium  vapor,  though  there  are  three  different  radiations, 
these  three  are  all  so  nearly  homogeneous  that  each  one  can 
be  used;  and  the  complexity  of  the  spectrum  is  in  this  case 
an  advantage,  as  will  be  shown  below.  To  produce  the  cad- 
mium radiation,  metallic  cadmium  is  placed  in  a  glass  tube 
which  contains  two  aluminum  electrodes.  The  tube  is  then 
connected  by  glass  tubing  with  an  air  pump  and  exhausted 
of  air.  The  tube  is  also  heated  so  as  to  drive  off  all  residual 
gas  and  vapor,  and  when  the  required  degree  of  exhaustion 
is  reached,  it  is  hermetically  sealed  and  in' condition  to  use. 
The  cadmium  is  not  very  volatile,  and  at  ordinary  tempera- 
tures we  should  see  scarcely  anything  of  the  cadmium  light 
when  the  electric  discharge  passes.  The  tube  is  therefore 
placed  in  a  metal  box,  as  shown  in  Fig.  60,  which  is  furnished 
with  a  window  of  mica  and  has  a  thermometer  introduced  into 
one  side.  If  the  box  be  heated  by  a  Bunsen  burner  to  a 
temperature  in  the  neighborhood  of  300°  C,  the  cadmium 
vapor  fills  the  tube,  and  can  then  be  rendered  luminous  by 
the  passage  of  the  electric  spark. 

Now,  it  is  found  most  convenient  not  to  make  this  first 
intermediate  standard  in  the  form  of  a  bar  like  the  standard 
meter,  with  two  lines  drawn  upon  it ;  for  then  we  should  intro- 
duce errors  of  the  microscope  at  every  reading,  and  these 
errors  would  be  added  together.  Thus,  since  this  is  one- 
tenth  of  the  whole  meter,  we  might  have,  in  adding  up,  ten 
times  the  error  of  the  microscope,  which  we  said  was  of  the 
order  of  one-half  a  micron ;  we  could  thus  have,  in  the  end, 
an  error  of  five  microns.  The  interference  method  gives  us 
the   means   of  multiplying   the  length  of   the  intermediate 


Light  Waves  as  Standards  of  Length        93 

standard  with  the  slightest  possible  error,  amounting,  per- 
haps, to  one -twentieth  of  a  micron ;  in  some  cases  a  little  less. 
If  two  plane  surfaces  be  parallel  to  one  another  and  a  given 
distance  apart,  then,  with  the  interferometer,  we  may  locate 
the  position  of  either  one  of  these  surfaces  by  means  of 
the  interference 
fringes  in  white 
light  to  within 
one-twentieth  of 
a  fringe,  which 
means  one-for- 
tieth of  a  wave, 
or  one-eightieth 
of  a  micron.  It 
has  been  found  fiq_  70 

most  convenient 

to  use  glass  surfaces  very  carefully  polished  and  made  as 
nearly  plane  as  possible,  and  silvered  on  the  front.  The 
two  surfaces  are  mounted  on  a  brass  casting,  and  care- 
fully adjusted  so  as  to  be  as  nearly  parallel  as  possible, 
so  that  it  does  not  matter  what  part  of  the  surface  is  used. 
This  parallelism  of  the  two  surfaces  must  be  arranged 
with  extraordinary  accuracy;  the  greatest  deviation  from 
true  parallelism  must  be  of  the  order  of  one-half  of  a 
fringe,  which  would  be  one -fourth  of  a  wave  length,  or 
one -eighth  of  a  micron.  Since  the  width  of  the  surface 
is  something  like  two  centimeters,  the  allowable  angle 
between  the  two  surfaces  is  something  like  one  part  in 
two  hundred  thousand. 

A  section  of  the  intermediate  standard  we  have  been  de- 
scribing is  represented  in  Fig.  70.  The  two  glass  surfaces 
are  about  two  centimeters  square  and  silvered  on  their  front 
surfaces,  which  are  very  nearly  true  planes.  Their  rear 
surfaces  press  against  three  small  pins.     These  are  adjusted 


94 


Light  Waves  and  Theik  Uses 


FIG.  71 


for  parallelism  by  tiling  until  the  requisite  degree  of  accuracy 
is  obtained.  The  parallelism  cannot  be  made  altogether 
perfect,  and,  as  a  matter  of  fact,  in  some  cases  the  error  may 
amount  to  as  much  as  one-tenth  of  a  micron  or  more. 

Fig.  71  represents  a  perspective  view  of  the  same  thing. 

In  this  tigure 
the  intermedi- 
ate standard 
rests  on  a  car- 
riage by  means 
of  which  it  may 
be  moved  as 
necessary  for 
the  purpose  of 
comparing  it 
with  the  whole 
meter.  In  mak- 
ing this  comparison  the  surfaces  must  be  parallel  to  the  mirror 
which  serves  as  a  reference  plane  in  the  interferometer.  The 
parallelism  in  this  case  must  be  of  the  same  order  of  accu- 
racy as  that  between  the  surfaces  themselves.  The  adjust- 
ment is  made  by  the  screws  at  the  rear,  one  of  which  turns 
the  whole  standard  about  a  vertical  axis  and  the  other  about 
a  horizontal  one. 

In  determining  the  number  of  waves  in  the  meter,  the 
first  operation  is  to  find  the  number  of  whole  waves  in  this 
intermediate  standard.  It  can  readily  be  conceived  that  the 
counting  of  something  like  300,000  waves  would  be  no  small 
matter;  in  fact,  a  little  calculation  would  show  that,  if  we 
counted  two  per  second,  it  would  take  over  forty  hours 
to  make  the  count.  Probably  a  number  of  methods  will 
suggest  themselves  of  making  such  a  process  of  counting 
automatic.  Indeed,  several  experiments  have  been  made, 
and  with    some    promise    of    success ;    but    the    possibility 


Light  Waves  as  Standakds  of  Length   95 

of  skipping  over  one  fringe,  through  some  accident,  is 
serious.  It  was  therefore  thought  desirable  to  use  another 
process,  very  much  longer  and  more  tedious,  but  very  much 
surer.  This  process  consists  in  dividing  the  distances  to  be 
measured  into  a  very  much  smaller  number  of  parts,  so  that 
the  distances  to  be  measured  in  waves  would  be  very  much 
smaller.  Thus  a  distance  of  ten  centimeters  contains  300.- 
000  waves;  half  of  this  distance  would  contain  150,000.  If 
we  go  on  dividing  in  this  way,  until  we  get  to  the  last  one 
of  nine  such  steps,  we  reach  an  intermediate  standard  whose 
length  is  something  of  the  order  of  one-half  millimeter. 
The  total  number  of  waves  in  this  standard  is  about  1,200, 
and  this  number  it  is  a  comparatively  simple  matter  to  count. 
The  method  of  proceeding  in  counting  these  fringes 
is  the  same  as  that  described  above.  The  reference  plane, 
as  we  will  call  the  movable  mirror  in  the  interferometer, 
is  moved  gradually  from  coincidence  with  the  first  sur- 
face to  coincidence  with  the  second,  and  the  fringes  which 
pass  are  counted.  Such  a  count  was  made  for  the  three 
standard  radiations,  namely,  the  red,  green,  and  blue  of 
cadmium  vapor.  The  result  was  1,212.37  for  red,  1,534.79 
for  green,  and  1,626.18  for  blue.  Now,  an  important  point 
is  that  we  can  measure  these  fractions  with  an  extraordi- 
nary degree  of  accuracy;  so  the  second  decimal  place  is 
probably  correct  to  within  two  or  three  units.  The  whole 
number  we  know  to  be  correct  by  repeating  the  count  and 
getting  the  same  result.  Having  thus  obtained  this  number, 
including  also  the  fractions  of  waves  on  the  shorter  standard 
to  a  very  close  approximation,  we  compare  it  with  the 
second,  which  is,  approximately,  twice  as  long.  This  com- 
parison gives  us,  without  further  counting,  the  whole  number 
of  waves  in  the  second  standard  by  multiplying  the  number 
in  the  first  by  two.  We  have  the  same  possibility  of  meas- 
uring fractions  on  the  second  standard,  and  so  can  determine 


96 


Light  Waves  and  Their  Uses 


the  number  of  waves  in  its  length  with  an  equal  degree  of 
accuracy. 

I  will  give  the  description  of  this  process  somewhat  more 
in  detail.      In  Fig.  72  mm'  represents  the  first  or  the  shorter 

standard  viewed 
from  above.  This 
standard  rests  on  a 
carriage  which  can 
be  moved  with  a 
screw.  The  second 
standard  im'  is  twice 
as  long  as  the  first, 
and  is  placed  as  close 
as  possible  to  the 
first  and  rigidly  con- 
nected with  some 
part  of  the  frame. 
The  mirror  d  is  the 
reference  plane.' 
The  two  front  mirrors  of  the  two  standards  are  adjusted  to 
give  fringes  in  white  light  with  the  reference  plane.  The 
central  fringe  in  the  white-light  system  is  black ;  the  others 
are  colored.  Hence  we  can  always  distinguish  the  central 
fringe.  When  the  central  fringes  occur  in  the  same  rela- 
tive position  upon  the  two  front  mirrors  7n  and  oi,  then 
these  two  surfaces  are  exactly  in  the  same  plane.  Now,  if  we 
move  the  reference  plane  backward  through  the  length  of  the 
shorter  standard,  its  surface  will  coincide  with  the  mirror  m', 
and  at  this  instant  fringes  in  white  light  will  appear.  Thus 
we  have  the  means  of  knowing  when  the  reference  plane 
has  been  moved  the  length  of  the  first  standard  to  an  order 
of  accuracy  of  one-tenth  or  one-twentieth  of  a  fringe. 


FIG.  72 


'  Better,  the  iniacje  of  d  in  <i  and  /^  which  in  the  figure  would  coincide  with  the 
front  surfaces  of  ni  and  n. 


Light  Waves  as  Standakds  of  Length        97 

The  next  process  is  to  move  the  first  standard  backward 
througli  the  same  distance.  Then  the  white-light  fringes 
will  again  appear  on  the  front  mirror  m.  Finally  we  move 
the  reference  plane  again  through  the  same  distance  and,  if 
the  second  standard  is  twice  as  long  as  the  first,  we  get  inter- 
ference fringes  on  the  two  rear  mirrors  of  the  two  interme- 
diate standards.  If  there  is  any  difference,  then  the  central 
fringe  of  the  white-light  system  will  not  be  in  the  same 
position  on  both  mirrors,  and  we  shall  know  that  one  is  twice 
as  long  as  the  other  less,  say,  two  fringes,  which  would  mean 
less  one-half  micron.  In  this  way  we  can  tell  whether  one  is 
exactly  twice  as  long  as  the  other  or  not;  and  if  not,  we  can 
determine  the  difference  to  within  a  very  small  fraction  of  a 
wave. 

When  we  multiply  the  number  of  waves  in  the  first 
standard  by  two,  any  error  in  the  fractional  excess  is,  of 
course,  also  multiplied  by  two.  So  the  fraction  of  a 
wave  which  must  be  added  to  the  second  number  is  uncer- 
tain. If  we  observe  the  fringes  produced  by  one  radiation, 
for  example  the  red,  we  get  a  system  of  circular  fringes  upon 
both  mirrors  of  the  standard ;  and  if  these  two  systems  have 
the  same  appearance  on  the  upper  mirror  as  on  the  lower, 
then  we  know  this  fraction  is  zero ;  and  the  number  of  waves 
in  the  second  standard  is  then  the  nearest  whole  number 
to  the  number  determined.  If  this  is  not  the  case,  we  can 
by  a  simple  process  tell  what  the  fraction  is,  and  can  obtain 
this  fractional  excess  to  any  required  degree  of  accuracy. 
As  an  example,  we  may  multiply  the  numbers  obtained  for 
the  first  standard  by  two,  and  we  find  2,424.74  for  the 
number  of  red  waves  in  standard  No.  2,  The  correct  value 
of  this  fraction  for  red  light  was  found  to  be  .93  instead  of 
.74.  Thus  the  same  degree  of  accuracy  which  was  obtained 
in  measuring  the  first  standard  can  be  obtained  in  all  the 
standards  up  to  the  last.      We  have  thus  the  means  of  find- 


98 


Light  Waves  and  Their  Uses 


ing  accurately  the  whole  number  of  waves  in  the  last 
standard.  The  whole  number  obtained  by  this  process  of 
"stepping  off"  for  the  red  radiation  of  cadmium  was  found 
to  be  310,678.  The  fraction  was  then  determined  by  the 
circular  fringes,  as  described  above,  and  found  to  be  .48. 
In  the  same  way  the  number  for  the  green  radiation  was 
determined  as  393,307.93;  and  for  the  blue  radiation  as 
416,735,86.  To  give  an  idea  of  the  order  of  accuracy, 
I  would  state  that  there  were  three  separate  determina- 
tions made  at  different  times  and  by  different  individuals, 
as  follows: 


Determination 

Red 

Green 

Blue 

I 

II 

Ill 

.310,678.48 
310,678.65 
310,678.68 

393,307.92 
393,-308.10 
393,308.09 

416,735.86 
416,736.07 
416,736.02 

The  fact  that  these  determinations  were  made  at  entirely 
different  times,  separated  by  an  interval  of  whole  months, 
and  by  different  individuals,  and  that  we  still  were  able  to 
get,  not  only  the  same  whole  number  of  waves,  but  also  so 
nearly  the  same  fractions,  gives  us  a  confidence,  which 
we  could  not  otherwise  feel,  in  the  possibilities  of  the 
process. 

In  comparing  the  standards  with  one  another  the  tem- 
perature made  no  difference,  if  only  it  were  uniform  through- 
out the  instrument,  because  two  intermediate  standards  side 
by  side,  made  of  the  same  substance,  would  expand  in  ex- 
actly the  same  way,  provided  we  could  be  sure  that  both  had 
the  same  temperature.  But  in  the  determination  of  the  num- 
ber of  waves  in  standard  No.  9  it  is  extremely  important 
to  know  the  tem|)erature  with  the  very  highest  degree  of 
accuracy.     For  this   purpose  some  of  the  best  thermome- 


Light  Waves  as  Standards  of  Length        99 

ters  obtainable  were  placed  in  the  instrument,  and  the 
thermometers  themselves  were  carefully  tested,  their  errors 
determined,  and  other  well-known  precautions  taken.  In 
this  way  the  temperature  at  which  the  intermediate  standard 
No.  9  contains  the  number  of  waves  given  above  was  deter- 
mined to  within  one-hundredth  of  a  degree. 

The  final  step  in  the  process  is  the  comparison  of  the 
decimeter  standard  with  the  standard  meter.  This  is  a  com- 
paratively simple  affair.  In  fact,  it  is  exactly  the  same  as 
the  comparison  of  the  first  intermediate  standard  with  the 
second,  except  that  the  second  standard  is  now  ten  times  as 
long  —  which  necessitates  going  through  the  process  ten 
times  instead  of  twice. 

Since  in  this  case  also  we  use  the  fringes  for  determining 
when  one  end  of  the  standard  and  the  reference  plane  are 
in  the  same  plane,  the  error,  as  before  stated,  may  be  as 
small  as  one-twentieth  of  a  wave;  so  that  all  the  errors  added 
together  would  be  of  the  order  of  one-half  of  a  wave,  or 
one  quarter  of  a  micron. 

The  conditions  which  had  to  be  fulfilled  by  the  instru- 
ment which  was  used  for  this  purpose  are,  then,  these:  We 
have,  in  the  first  place,  to  provide  for  the  displacement  of 
the  intermediate  standard  and  of  the  reference  plane  in  such 
a  way  that  the  parallelism  of  the  mirrors  is  not  disturbed. 
This  necessitates  that  the  ways  along  which  the  carriage 
supporting  the  mirrors  moves  be  exceedingly  true.  It  took 
a  whole  month  to  perform  this  part  of  the  work  —  to  get  the 
ways  so  nearly  true  that  there  should  be  no  change  in  the 
position  of  the  fringes  as  the  mirrors  were  moved  back  and 
forth.  In  the  second  place,  we  must  be  able  to  know  the 
position  of  the  mirrors  inside  of  the  box  which  is  placed 
over  the  instrument  to  protect  it  from  temperature  changes. 
To  secure  this,  the  carriage  which  holds  the  mirrors  must  be 
moved  by  means   of  a  long   screw   carefully   calibrated    to 


100 


Light  Waves  and  Their  Uses 


within  two  microns  or  so.  In  the  third  place,  since  there 
will  be  slight  displacements,  owing  to  the  impossibility  of 
getting  the  ways  absolutely  true,  it  must  be  possible  to  cor- 
rect these  displacements.  The  adjustments  for  effecting  this 
are  shown  in  Fig.  71.  Fourth,  we  must  have  a  firm  sup- 
port for  the  longer  of  the  two  standards  to  be  compared. 


-^ 


'^^ 


0        Xz>, 


FIG.  73 

and  a  movable  support,  which  moves  parallel  with  itself,  for 
the  shorter  standard. 

The  last  standard,  the  auxiliary  meter,  has  to  be  com- 
pared with  the  standard  meter  itself,  and,  therefore,  the  two 
must  be  of  similar  construction.  In  other  words,  in  this 
last  comparison  we  have  to  resort  to  the  microscope  again. 
For  the  meter  bar  which  we  had  in  the  interferometer  itself 
had  two  lines  upon  it  as  nearly  as  possible  one  meter  apart, 
as  determined  by  a  rough  comparison  with  the  prototype 
meter.  The  standard  No.  9  had  to  be  compared  with 
this.  For  this  purpose  an  arm  which  had  a  fine  mark  on 
it  was  rigidly  fastened  to  the  standard  No.  9,  and  arranged  to 
come  in  the  focus  of  the  microscope.  In  making  this  com- 
parison, we  must  admit,  the  order  of  accuracy  is  not  so  great. 


Light  Waves  as  Standards  of  Length      101 

But  there  are  only  two  of  these  to  make,  so  that  the  possible 
error  is  the  same  as  that  to  which  we  are  liable  in  comparing 
two  meter  bars.     This  error  is  unavoidable. 

The  whole  instrument  had  to  be  placed  in  a  box,  which 
protected  it  from  temperature  changes  and  drafts  of  air,  and 
had  to  be  placed  on  a  firm  pier  so  as  to  keep  it  as  free  from 


FIG.  74 

vibration  as  possible.  Finally,  the  conditions  which  have  been 
mentioned  above  for  producing  a  suitable  source  of  light 
had  to  be  fulfilled.  We  have  thus  a  fair  idea  of  what  condi- 
tions had  to  be  met  in  constructing  the  complete  apparatus 
for  making  this  comparison. 

We  shall  now  show  how  these  conditions  were  actually 
fulfilled  in  the  apparatus  that  was  used  for  the  experiment. 

Fig.  73  gives  a  plan  of  the  entire  arrangement.  It  is 
easy  to  recognize  the  vacuum  tube  which  serves  as  a 
source  of  light  and  the  arrangement  of  the  plates  in  the 
interferometer.  This  arrangement  is  the  same  as  that 
shown  in  Figf.  72.  In  order  to  have  but  one  radiation  at  a 
time  in  the  instrument,  the  light  from  the  tube  is  passed 


102 


Light  Waves  and  Their  Uses 


through  an  ordinary  spectroscope.  Thus  the  light  from  the 
tube  Z  is  brought  to  a  focus  on  the  slit  i^-  I^  is  then  made 
parallel  by  means  of  the  lens  x-i  and  passes  through  the 
prism  W,  which  is  filled  with  bisulphide  of  carbon.     The 

lens  a?3  forms  the 
spectral  images 
of  the  slit  /i  in 
the  plane  of  the 
slit  t-i-  The  arm 
ZW oi  the  spec- 
troscope can  be 
moved  so  as  to 
bring  either  the 
red,  the  green, 
or  the  blue  spec- 
tral image  upon 
this  slit,  from 
which  it  passes 
into  the  instru- 
ment. 

Fig.  74  is  a 
view  of  the  plan 
of  part  of  the  in- 
strument. The 
arrangement  of 
surfaces  shown  diagramatically  in  Fig.  72  is  readily  recog- 
nized. All  of  the  plates,  I  may  state,  instead  of  being 
rectangular,  have  a  circular  border,  because  in  this  form 
they  can  be  worked  true  more  readily. 

Fig.  75  represents  a  vertical  cross-section  of  the  same  in- 
strument. It  will  be  noted  that  the  reference  plane  is  divided 
into  sections.  This  is  done  in  order  to  enable  us  to  determine 
very  accurately  the  position  of  the  interference  fringes.  The 
two  intermediate  standards  will  be  recognized  at  the  right. 


FIG.  7.-, 


Light  Waves  as  Standards  of  Length      103 

Fig.  76  represents  the  actual  instrument  in  perspective. 
In  this  the  two  microscopes,  with  their  arrangement  for  pro- 
ducing an  illumination  on  the  meter  bar  by  means  of  reflected 
light,  are  shown.  On  the  left  are  the  handles  which  turn  the 
two  screws.     One  of  these  moves  the  intermediate  standard 


FIG.  76 


and  the  other  moves  the  reference  plane.  The  complete 
instrument  in  the  case  which  protects  it  against  tempera- 
ture changes  is  shown  in  Fig.  77. 


This  investigation  was  reported  in  the  spring  of  1892  to 
Dr.  Gould,  who  at  that  time  represented  the  United  States  in 
the  International  Committee  of  Weights  and  Measures.  It 
was  principally  through  his  goodness  that  I  was  asked  to 
carry  out  the  actual  experiments  at  the  International  Bureau 
of  W^eights  and  Measures  at  Sevres.  Many  of  the  acces- 
sories that  were  required  for  the  instrument  which  has  just 
been  described  had  to   be  made  in   this  country,  and  were 


104 


Light  Waves  and  Theik  Uses 


taken  over  and  installed  in  one  of  the  laboratories  of  the 
Bureau. 

The  standard  meter  itself  is  kept  in  a  vault  underground 
and  under  double  lock  and  key,  and  is  inspected  only  once 
in  ten  years,  and  even  then  it  is  not  handled  any  more  than 


FIG.  77 

is  absolutely  necessary.  It  took  the  better  part  of  an  entire 
year  to  accomplish  the  work  as  it  has  been  described.  The 
final  result  of  the  investigation  was  that  the  number  of 
light  waves  in  a  standard  meter  was  found  to  be,  for  the  red 
radiation  of  cadmium  1,553,163.5,  for  the  green  1,966,249.7, 
for  the  blue  2,083,372.1— all  in  air  at  15°  C.  and  at  normal 
atmospheric  pressure. 

It  is  also  worth  noting  that  the  fractions  of  a  wave  are 
important,  because,  while  the  absolute  accuracy  of  this 
measurement  may  be  roughly  stated  as  about  one  part  in 
two  million,  the  relative  accuracy  is  much  greater,  and  is 
probably  about  one  part  in  twenty  million. 


Light  Waves  as  Standards  of  Length      105 

The  question  may  be  asked:  What  is  the  object  of  mak- 
ing such  determinations,  when  we  know  that  the  standard 
itself  would  not  change  by  any  amount  which  would  vitiate 
any  ordinary  measurements  ?  The  reply  would  be  that, 
while  the  care  taken  of  the  standards  is  pretty  sure  to  secure 
them  from  any  serious  accident,  yet  we  have  no  means  of 
knowing  that  any  of  these  standards  are  hot  going  through 
some  slow  process  of  change,  on  account  of  a  gradual 
rearrangement  of  the  molecules.  Now  that  we  have  com- 
pared the  meter  with  an  invariable  standard,  we  have  the 
means  of  detecting  any  slow  change  and  of  correcting  the 
standard  which  has  been  vitiated  by  such  process.  Thus  it 
is  now  possible  to  control,  by  reference  to  the  standard  light 
waves,  the  standard  of  length.  The  standard  light  waves 
are  not  alterable ;  they  depend  on  the  properties  of  the  atoms 
and  upon  the  universal  ether ;  and  these  are  unalterable.  It 
may  be  suggested  that  the  whole  solar  system  is  moving 
through  space,  and  that  the  properties  of  ether  may  differ 
in  different  portions  of  space.  I  would  say  that  such  a 
change,  if  it  occurs,  would  not  produce  any  material  effect  in 
a  period  of  less  than  twenty  millions  of  years,  and  by  that 
time  we  shall  probably  have  less  interest  in  the  problem. 

SUMMARY 

1.  We  find  that  three  propositions  for  expressing  our 
standard  of  length  in  terms  of  some  invariable  length  in 
nature  have  been  made,  namely: 

a)  Measurement  of  the  seconds  pendulum. 

6)   Measurement  of  the  earth's  circumference. 

c)  Measurement  of  light  waves. 

The  first  two,  as  well  as  the  first  plan  proposed  for  carry- 
ing out  the  third,  i.  e.,  the  method  of  the  diffraction  grating, 
have  been  found  deficient  in  accuracy. 

2.  The  second  or  interference  method  of  utilizing  light 


106  Light  Waves  and  Theie  Uses 

waves,  while  ideally  simple  in  theory,  necessitates  in  practice 
an  elaborate  and  complicated  piece  of  apparatus  for  its 
realization.  But,  notwithstanding  the  delicacy  of  the  opera- 
tion, it  is  capable  of  giving  results  of  such  extraordinary 
accuracy  that,  were  the  fundamental  standard  lost  or  de- 
stroyed, it  could  be  replaced  by  this  method  with  duplicates 
which  could  not  be  distinguished  from  the  originals. 


LECTUEE   VI 

ANALYSIS    OF    THE    ACTION    OP    MAGNETISM    ON    LIGHT 
WAVES  BY  THE  INTERFEROMETER  AND  THE  ECHELON 

A  LITTLE  over  a  year  ago  the  scientific  world  was  startled 
by  the  announcement  that  Professor  Zeeman  had  discovered 
a  new  effect  of  magnetism  on  light.  The  experiment  that 
he  tried  may  be  briefly  described  in  the  following  way:  If 
we  place  a  sodium  flame  in  front  of  the  slit  of  a  spectroscope, 
we  get  in  the  field  of  view  a  bright  double  line.  If  the  flame 
is  placed  between  the  poles  of  a  powerful  electro-magnet,  it  is 
found  that  the  lines  are  very  much  broadened;  at  least  this 
was  the  way  in  which  the  announcement  of  the  discovery  was 
first  made.  It  may  be  mentioned  that  a  somewhat  similar 
observation  was  made  by  M.  Fievez  a  long  time  before.  He 
found  that  the  sodium  lines  in  the  spectrum  were  modified  by 
the  magnetic  field,  but  not  quite  in  the  way  that  Zeeman 
announced ;  instead  of  the  lines  being  broadened,  he  thought 
that  each  separate  sodium  line  was  doubled  or  quadrupled.  It 
seems  that,  long  before  this,  the  experiment  had  actually  been 
tried  by  Faraday,  who,  guided  by  theoretical  reasons,  con- 
jectured that  there  should  be  some  effect  produced  by  a 
powerful  magnetic  field  upon  radiations. 

The  only  reason  why  Faraday  did  not  succeed  in  observ- 
ing what  Fievez  and  Zeeman  observed  afterward  was  that  the 
spectroscopic  means  at  his  disposal  at  the  time  were  far  from 
being  sutficiently  powerful.  The  effect  is  very  small  at  best. 
The  distance  between  the  sodium  lines  being  taken  as  a  kind 
of  unit  for  reference,  the  separate  sodium  lines,  as  was  shown 
in  a  preceding  lecture,  have  a  width  of  about  one -hundredth 
of    the    distance    between    the    two.      The    broadening,  or 

107 


108  Light  Waves  and  Their  Uses 

doubling,  or  other  modification  whicli  is  produced  in  the 
spectrum  by  the  magnetic  field,  is  of  the  order  of  one-fortieth, 
or  perhaps  one-thirtieth,  of  the  distance  between  the  sodium 
lines.  Hence,  in  order  to  see  this  efi^ect  at  all,  the  highest 
spectroscopic  power  at  our  disposal  must  be  employed. 
Subsequent  investigation  has  shown,  indeed,  that  still  other 
modifications  ensue,  which  are  very  much  smaller  even  than 
this,  and  which  cover  a  space  of  perhaps  only  one-hundredth 
to  one  hundred-and-fiftieth  of  the  distance  between  the  so- 
dium lines.  They  are,  therefore,  beyond  reach  of  the  most 
powerful  spectroscope. 

It  occurred  to  me  at  once  to  try  this  experiment  by  the 
interference  method,  which  is  particularly  adapted  to  the 
examination  of  just  such  cases  as  this,  in  which  the  effect  to 
be  observed  is  beyond  the  range  of  the  spectroscopic  method. 
The  investigation  was  repeated  in  very  much  the  same  way 
as  described  by  Zeeman,  namely:  A  little  blow-pipe  flame 
w^as  placed  between  the  poles  of  a  powerful  electro-magnet; 
a  piece  of  glass  was  placed  in  the  flame  to  color  it  with  so- 
dium light.  The  light,  instead  of  passing  into  the  spectro- 
scope, was  sent  into  an  interferometer  and  analyzed  by  the 
method  described  in  Lecture  IV.  The  visibility  curves 
which  were  thus  obtained  showed  that,  instead  of  a  broad- 
ening, as  was  first  announced  by  Zeeman,  each  of  the  so- 
dium lines  appeared  to  be  double.  The  visibility  curves 
which  were  observed  are  shown  in  Fig.  78,  and  in  Fig.  79, 
the  curves  which  give  the  corresponding  distribution  of  the 
light  in  the  source.  In  the  former  figure  the  vertical 
distances  of  the  different  curves  represent  the  clearness  of 
the  fringes,  and  the  horizontal  distances  the  differences 
in  path.  In  curve  A,  as  the  difference  in  the  paths 
increases,  the  fringes  become  less  and  less  distinct,  until  at 
forty  millimeters  the  fringes  have  almost  entirely  disap- 
peared.    This  curve  represents  the  visibility  of  the  sodium 


Action  of  Magnetism  on  Light  Waves      109 


flame  without  any  magnetic  field.  The  corresponding 
intensity  curve  A  (Fig,  79)  shows  that  the  center  of  the  line 
has  the  greatest  in- 
tensity and  that  the 
intensity  falls  off  rap- 
idly on  either  side, 
the  width  of  the  line 
corresponding  to 
something  like  one- 
hundredth  of  the  dis- 
tance between  the  two 
sodium  lines.  When 
the  field  was  created 
by  simply  closing  the 
current  through  the 
magnet,  the  visibility 
curve  assumed  the 
form  indicated  in 
curve  B.  The  cor- 
responding distribu- 
tion of  light  is  shown  in  the  second  of  the  intensity 
curves,  B  (Fig.  79)  and  we  see  that  the  line  shows  simply  a 
broadening,  with   a  possible  indication  of  doubling.     The 

field  was  then  increased 
considerably ;  curve  C 
(Fig.  78)  represents  the 
visibility.  The  corre- 
sponding intensity  curve 
shows  clearly  that  the 
line  is  double.  The 
other  curves  were  ob- 
tained by  increasing 
the  field  gradually,  and  it#  will  be  noted  that  the  result 
is  an  increasing   separation  of   the   line    and,   at   the   same 


FIG.  78 


fig.  79 


110  Light  Waves  and  Their  Uses 

time,  a  considerable  broadening  out  of  the  two  separate 
elements. 

This  same  experiment  was  tried  with  other  substances, 
especially  with  cadmium,  and  it  was  found  that  almost  iden- 
tical results  were  obtained  with  cadmium  light  as  with 
sodium.  It  was  therefore  inferred  that  the  observations  an- 
nounced by  Zeeman  were,  at  any  rate,  incomplete,  and  it 
was  thought  that  possibly  the  instruments  at  his  command 
were  not  sufficiently  powerful  to  show  the  phenomena  of  the 
doubling.  Shortly  after  this  experiment  was  published  an- 
other announcement  was  made  by  Zeeman.  In  this  he  states 
that  there  is  not  simply  a  broadening  of  the  lines,  but  a  sepa- 
ration of  them  into  three  components,  and,  what  was  very 
much  more  interesting,  that  these  three  components  are 
polarized  in  directions  at  right  angles  with  each  other:  the 
middle  line  polarized  in  one  plane  and  the  two  outer  lines 
in  another. 

To  make  the  meaning-  of  this  clear,  we  shall  have  to  make 
a  brief  digression  into  the  subject  of  the  polarization  of 
light.  It  will  be  remembered  that  in  one  of  the  first 
illustrations  of  wave  motion  light  waves  were  compared 
with  the  waves  along  a  cord,  and  it  was  stated  that 
the  vibrations  which  caused  the  phenomena  of  light  are 
known  to  be  vibrations  of  this  character  rather  than  of  the 
character  of  sound  waves.  The  sound  waves  consist  of 
vibrations  in  the  direction  of  the  propagation  of  the  sound 
itself.  The  motion  of  the  particles  in  the  light  waves  are 
at  right  angles  to  their  direction  of  propagation.  These 
transverse  vibrations,  as  they  are  called,  may  be  vertical  or 
horizontal,  or  they  may  be  diagonal,  or  they  may  move  in  a 
curved  path,  for  instance  in  circles  or  ellipses. 

In  the  case  of  ordinary  light  the  vibrations  are  so  mixed 
up  together  in  all  possible  planes- that  it  is  impossible  to  sepa- 
rate   any   one    particular  vibration    from   the   rest   without 


Action  op  Magnetism  on  Light  Waves      111 

special  devices,  and  such  devices  are  termed  "  polarizers." 
They  may  be  likened  very  roughly  to  a  grating  the  aper- 
tures of  which  determine  the  plane  of  vibration.  Through 
such  a  grating  we  can  transmit  vibrations  along  a  cord  only 
in  the  plane  of  the  apertures.  A  vibration  at  right  angles 
to  this  plane  will  not  travel  along  the  cord  beyond  the  grat- 
ing. The  corresponding  light  phenomena  may  be  illustrated 
by  attempting  to  pass  a  beam  of  light  which  has  been  polar- 
ized through  a  medium  which  acts  toward  the  light  waves 
as  does  the  grating  toward  the  waves  on  the  cord.  It 
is  found  that  crystals  act  as  such  media.  Thus  a  plate 
of  tourmaline  possesses  this  property.  For,  as  is  well 
known,  if  two  plates  of  tourmaline  be  placed  so  that  their 
optical  axes  are  parallel  with  each  other,  almost  as  much 
light  will  pass  through  the  two  as  through  either  one  alone. 
But  if  the  axes  are  set  at  right  angles  to  each  other  by  turn- 
ing one  of  them  through  90°,  the  light  is  entirely  cut  off. 
Turning  again  through  90°,  the  light  again  appears,  etc. 
In  the  case  of  the  tourmaline  the  vibrations  which  have 
passed  through  one  plate  are  all  in  one  plane. 

There  is  another  important  case  in  which  the  light  is  said 
to  be  polarized,  namely,  when  the  motion  of  the  particles  is 
circular.  We  may  have  two  such  circular  vibrations  —  one  in 
which  the  motion  is  in  the  direction  of  the  hands  of  a  watch, 
called  right-handed,  and  the  other  in  which  the  motion  is  in 
the  direction  opposite  to  that  of  the  hands  of  a  watch,  and 
which  is  therefore  called  left-handed.  We  may  consider  that 
each  one  of  these  vibrations  is  compounded  of  two  plane 
vibrations  of  equal  intensity,  in  one  of  which  the  motion  is 
horizontal  and  in  the  other  vertical,  and  which  differ  from  one 
another  in  phase,  this  difference  being  one-fourth  of  a  period 
for  the  left-handed  and  three-fourths  of  a  period  for  the  right- 
handed.  If  we  add  together  two  such  circular  vibrations 
of  equal  intensity,  their  horizontal  components  would  exactly 


112 


Light  Waves  and  Theik  Uses 


neutralize  each  other,  so  that  there  would  be  no  horizontal 

motion  at  all.      The  vertical  components,  however,  being  in 

the  same  direction,  will  add  to  each  other, 

■     so  that  the  resultant  of  two  beams  of  light 
polarized  circularly  in  opposite  directions 
and  of  equal  intensity  is  a  plane  polarized 
ray. 
To  return,  now,  to  Zeeman's  phenome- 


FIG. 


lines  when  examined  in  a  direction  at  right 
angles  to  the  magnetic  field.  The  upper 
line  represents  the  appearance  when  the 
light  is  polarized  so  that  only  horizontal 
vibrations  reach  the  spectroscope.  If, 
however,  the  polarizer  is  rotated  through  90°,  so  that  only 
vertical  vibrations  pass,  the  appearance  is  that  of  the  lower 
half  of  the  diagram,  the  two  side  lines  appearing  and  the 
central  line  disappearing.  Finally,  if  the  light  is  examined 
in  the  direction  of  the  magnetic  field,  which  can  be  accom- 
plished by  boring  a  hole  through  the  pole  of  the  magnet, 
it  is  found  that  only  two  are  visible  —  the  two  outside  ones; 
and  one  of  these  is  composed  of  light  which  vibrates  cir- 
cularly in  the  direction  of  the  hands  of  a  watch,  and  the 
other  is  circularly  polarized  in  the  opposite 
direction. 

An  extremely  beautiful  and  simple  ex- 
planation of  this  phenomenon  has  been 
given  by  Lorentz,  Larmor,  Fitzgerald,  and 
a  number  of  others.  At  the  risk  of  intro- 
ducing a  few  technicalities,  I  will  venture 
to  repeat  this  explanation  in  a  simple  form. 
For  this  purpose  it  is  necessary  to  know  that 
the  particles  or  atoms  of  matter  are  each  supposed  to  be  asso- 
ciated with  an  electric  charge,  and  that  such  a  charged  par- 


FIG.  81 


Action  of  Magnetism  on  Light  Waves      113 

tide  is  termed  an  "electron."  This  hypothesis,  made  long 
before  Zeeman  made  his  discovery,  was  found  necessary  to 
account  for  the  facts  of  electrolysis.  For  the  decomposition 
of  an  electrolyte  by  an  electric  current  is  most  simply 
explained  upon  the  hypothesis  that  it  contains  positively 
and  negatively  charged  particles,  and  that  the  positively 
charged  atoms,  go  toward  the  negative  pole,  and  the  nega- 
tively charged  toward  the  positive  pole.  They  then  give 
up  their  electricity,  and  this  giving  up  of  electricity  consti- 
tutes an  electric  current.  Hence  this  assumption,  which  is 
useful  in  explaining  the  Zeeman  effect,  is  nothing  new.  It 
is  known,  also,  that  the  vibrations  of  these  particles,  or  of 
their  electric  charges,  produce  the  disturbance  in  the  ether 
which  is  propagated  in  the  form  of  light  waves;  and  that 
the  period  of  any  light  wave  corresponds  to  the  period  of 
vibration  of  the  electric  charge  which  produces  it. 

The  most  general  form  of  path  of  such  a  vibrating 
electric  charge  would  be  an  ellipse.  Now,  an  elliptical  vibra- 
tion can  always  be  resolved  into  a  circular  vibration  and  a 
plane  one,  so  that  any  polarized  ray  may  be  resolved  into  a 
plane  polarized  ray  and  a  circularly  polarized  ray.  So  all 
we  need  to  consider  are  plane  and  circularly  polarized  rays. 
But  we  may  suppose  that  a  plane  vibration  is  due  to  two 
oscillations  in  a  circle,  one  going  in  a  direction  opposite  to 
that  of  the  hands  of  a  watch,  and  the  other  in  their  direction. 
Hence,  we  need  consider  only  circular  vibrations.  Now, 
if  the  electric  charge  is  moving  in  a  circle,  it  can  be  shown 
that  when  the  plane  of  the  circle  is  at  right  angles  to  the 
direction  between  the  two  poles  of  the  magnet,  the  effect  of  the 
field  would  be  to  accelerate  the  motion  when  the  rotation  is, 
say,  counter-clockwise,  but  to  retard  it  when  it  is  clockwise. 

It  was  shown  above  that  the  position  of  a  spectral  line 
in  the  spectrum  depends  on  the  period  of  the  light  which 
produces  it.     Hence  the  position  of  the  line  will  be  altered 


114  Light  Waves  and  Their  Uses 

when  any  current  is  passing  about  the  electro-magnet.  When 
the  current  is  passing  in  a  certain  direction,  the  velocity  of 
rotation  of  the  particles  moving,  say  counter-clockwise,  is 
increased.  Hence  the  period  of  vibration  is  smaller;  i.  e., 
the  number  of  vibrations,  or  the  frequency,  is  greater.  In 
this  case  there  will  be  a  shifting  toward  the  blue  end  of 
the  spectrum  by  an  amount  corresponding  to  the  amount  of 
the  acceleration.  Those  particles  which  are  rotating  in  an 
opposite  direction,  i.  e.,  clockwise,  will  be  retarded,  the 
frequency  will  be  less,  and  the  spectral  lines  will  be  shifted 
toward  the  red.  These  two  shiftings  would  account,  then, 
for  the  double  line.  It  is  further  clear  that  those  vibrations 
which  occurred  in  planes  parallel  to  the  lines  of  force  of  the 
magnetic  field  would  be  unaltered.  These  vibrations  would 
then  produce  the  middle  line,  which  is  not  shifted  from  its 
position  by  the  magnetic  field. 

Again,  if  we  are  viewing  the  light  in  a  direction  at  right 
angles  to  the  lines  of  force  of  the  field,  the  vibrations  of 
those  particles  which  are  affected  by  the  field  would  have  no 
components  parallel  to  the  field.  If  the  particles  are  re- 
volving in  a  plane  perpendicular  to  the  field,  then,  when 
viewed  in  this  direction,  they  would  appear  to  be  moving 
only  up  and  down;  i.  e.,  they  would  send  out  plane  polarized 
lio-ht  whose  vibrations  are  vertical.  These  two  vertical  vibra- 
tions  form  the  two  outer  lines  of  the  triplet,  and  it  can  be 
shown  that  the  light  is  plane  polarized  by  passing  it  through 
a  polarizer.  Those  particles  which  are  vibrating  horizontally 
do  not  have  their  period  of  vibration  altered  by  the  field. 
Consequently  we  get  a  single  line  whose  position  in  the 
spectrum  is  not  changed,  and  which  is  plane  polarized  in  a 
plane  at  right  angles  to  that  of  the  other  two. 

When  this  second  announcement  of  Zeeman  appeared, 
it  seemed  worth  while  to  repeat  the  experiments  with  the 


Action  of  Magnetism  on  Light  Waves      115 

interferometer,  especially  as  it  was  pointed  out  that  proba- 
bly the  reason  why  a  single  or  a  double  line  appeared, 
instead  of  a  triple  line,  was  because  part  of  the  light  corre- 
sponding to  the  middle  line  was  cut  off  by  the  reflection 
from  the  separating  plate  of  the  interferometer.  The  light 
thus  reflected  is  polarized,  and  most  of  the  light  which 
should  have  formed  the  central  image  is  thus  cut  off.  It 
was  therefore  determined  to  repeat  these  experiments  under 


N 


p 


FIG.  82 


such  conditions  that  we  could  be  perfectly  sure  that  light 
which  reached  the  interferometer  vibrated  in  only  one  plane. 
To  accomplish  this  it  is  necessary  merely  to  introduce  a 
polarizer  into  the  path  of  the  light. 

Fig.  82  represents  the  arrangement  of  the  experiment 
with  the  interferometer.  The  source  of  light,  instead  of 
being  sodium  in  a  Bunsen  flame,  is  vapor  in  a  vacuum  tube, 
illuminated  by  an  electric  discharge.  The  capillary  part  of 
the  tube  is  placed  between  the  poles  of  the  magnet. 

The  light  is  first  passed  through  an  ordinary  spectro- 
scope, so  that  there  is  formed  at  s  a  spectrum,  any  part  of 
which  we  may  examine.  The  slit  at  s  allow^s  only  one  radia- 
tion to  pass  into  the  interferometer.  Thus,  if  we  examine 
cadmium  light,  we  may  allow  the  red  to  pass  through,  or  the 
green,  or  the  blue.  The  light  is  made  parallel  by  a  lens  and 
then  passes  into  the  interferometer.     The  arrangement  for 


116 


Light  Waves  and  Their  Uses 


examining  separately  the  vertical  vibrations  alone  and  the 
horizontal  vibrations  alone  is  represented  at  N,  and  consists 
merely  of  a  Nicol  prism  which  can  be  rotated  about  a  hori- 
zontal axis. 

With  this  arrangement  a  different  set  of  visibility  curves 

was    obtained.       These    are 
shown  in  Figs.  83,  84,  85. 

The  upper  curve  of  Fig. 
83  represents  the  visibility 
curve  produced  by  the  hori- 
zontal vibrations  of  the  red 
cadmium  light  in  a  strong 
maOTietic  field.  For  the  ver- 
tical  vibrations  the  visibility 
curve  is  something  totally 
different,  and  is  shown  in  the 
lower  half  of  the  figure.  The 
effect  of  the  field  is  readily 
appreciated  by  comparing 
this  figure  with  Fig.  66,  which  corresponds  to  the  red  cad- 
mium line  without  any  magnetic  field. 

The  upper  curve  of  Fig.  8-4  represents  the  visibility  curve 
of  the  blue  cadmium  vapor  when  the  horizontal  vibrations 
only  are  allowed  to  pass  through.  When  vertical  vibrations 
only  are  allowed  to  pass  through,  the  curve  has  the  form 
shown  in  the  lower  half  of  the  figure. 

The  case  of  the  green  radiation,  when  there  is  no  field, 
is  shown  in  Fig.  67  above.  When  the  magnetic  field  is 
on,  and  when  the  horizontal  vibrations  only  are  allowed  to 
pass  through,  the  visibility  curve  has  the  form  of  the  upper 
curve  in  Fiaf.  85.  When  vertical  vibrations  are  allowed  to 
pass  through,  it  has  the  form  of  the  lower  curve. 

The  intensity  curves  corresponding  to  Figs.  83,  81,  and 
85  are  shown  in  Fig.  86.      The  upper  three  correspond  to 


FIG.  83 


Action  op  Magnetism  on  Light  Waves     117 


the  horizontal  vibrations,  while  the  lower  three  correspond 
to  the  vertical  vibrations.  In  the  case  of  the  red  radiations 
it  will  be  noted  that,  whether  there  is  a  magnetic  field  or 
not,  there  is  no  particular  change  for  red  cadmium  light 
when  the  horizontal  vibrations  alone  are  considered.  When 
the  field  is  on,  the  vertical 
vibrations  give  a  double  line, 
or  possibly  one  of  more  com- 
plex form. 

In  the  case  of  the  blue 
radiations,  however,  when 
there  is  a  magnetic  field  and 
only  horizontal  vibrations 
are  allowed  to  pass  through, 
the  line  is  double.  The 
doubling  is  very  distinct, 
and  the  separation  is  so  wide 
that  it  should  be  easily  seen 
by  means  of  the  spectroscope.  When  the  vertical  vibra- 
tions alone  are  allowed  to  pass  through,  there  is  a  very  much 
more  complicated  effect.  In  all  cases  we  can  see  that  the 
line  is  double,  as  in  the  case  of  red  cadmium  light,  but  in 
this  case  each  component  of  the  double  lines  is  at  least 
quadruple,  or  even  more  complex. 

In  the  case  of  the  green  radiation,  when  horizontal  vibra- 
tions only  are  considered,  we  have  a  triple  line  for  the  cen- 
tral line  of  the  Zeeman  triplet.  When  horizontal  vibrations 
alone  are  allowed  to  pass  through  without  a  magnetic  field, 
it  resembles  in  general  character  the  red  line  (c/.  Fig.  67). 
When  vertical  vibrations  are  examined  in  the  magnetic 
field,  the  line  is  highly  complex;  and  in  this  case  it  is  abso- 
lutely certain  that  each  of  the  components  of  the  double 
consists  of  at  least  three  separate  lines.  The  phenomenon 
is  perfectly  symmetrical  about  the  central  line. 


fig. 


118 


Light  Waves  and  Their  Uses 


It  appears  from  these  results  that  the  Zeeman  effect  is  a 
much  more  complex  phenomenon  than  was  at  first  supposed, 
and  therefore  the  simple  explanation  that  was  given  above 
no  longer  applies.  At  any  rate,  it  must  be  very  seriously 
modified  in  order  to  account  for  the  much  more  highly  com- 
plex character  of  the  phe- 
nomena, as  here  described. 
The  complete  theory  has  not 
yet  been  worked  out,  and 
meanwhile  we  must  gather 
whatever  information  we 
can  concerning  the  behavior 
of  as  many  different  radia- 
tions as  possible.  Every 
attempt  to  deduce  some  gen- 
eral law  which  will  cover 
all  cases  at  present  known 
has  thus  far  proved  unsuc- 
cessful. There  are  a  number  of  anomalies  which  seem  even 
more  difficult  to  account  for  than  the  doubling  of  this  middle 
line  and  the  multiplication  of  the  side  lines.  For  example,  in 
one  of  the  radiations  examined,  the  line  without  any  magnetic 
field  appeared  as  quadruple,  but  when  the  magnetic  field  was 
on,  it  appeared  as  a  single  line. 

There  are  quite  a  number  of  other  interesting  cases,  which 
we  have  not  time  to  consider  now.  The  explanation  of  these 
anomalies  will  probably  not  be  given  until  long  after  the 
explanation  of  the  doubling  and  tripling  and  multiplication 
of  separate  lines. 

The  examination  of  spectral  lines  by  means  of  the  inter- 
ferometer, while  in  some  respects  ideally  perfect,  is  still 
objectionable  for  several  reasons.  In  particular,  it  requires 
a  very  long  time  to  make  a  set  of  observations,  and  we  can 


Action  of  Magnetism  on  Light  Waves     119 

examine  only  one  line  at  a  time.  The  method  of  observa- 
tion requires  us  to  stop  at  each  turn  of  the  screw,  and  note 
the  visibility  of  the  fringes  at  each  stopping-place.  During 
the  comparatively  long  time  which  it  takes  to  do  this  the 
character  of  the  radiations  themselves  may  change.  Besides, 
we  have  the  trouble  of  translating  our  visibility  curves  into 
distribution  curves.  Hence  it  is  rather  easy  for  errors  to 
creep  in. 

On  account  of    these  limitations  of  the  interferometer 
method,  attention  was  directed  to  something  which  should 


../^  .Sr;, , -rJ  ,\./ 


Type  I. 


A^A,a/,m/\o. 


TypeU. 


/    i    3    * 


FIG.  86 


jB 

Typelir. 


be  more  expeditious,  and  the  most  promising  method  of 
attack  seemed  to  be  to  try  to  improve  the  ordinary  diffrac- 
tion grating.  The  grating,  as  briefly  explained  in  one  of 
the  preceding  lectures,  consists  of  a  series  of  bars  very  close 
together,  which  permit  light  to  pass  through  the  intervals 
between  them.  The  first  gratings  ever  made  were  of  this 
nature,  for  they  consisted  of  a  series  of  wires  wound  around 
two  screws,  one  above  and  one  below.  This  first  form 
of  grating  answered  very  well  for  the  preliminary  work, 
but  is  objectionable  because  the  interval  between  the 
wires  is  necessarily  rather  large,  /.  e.,  the  grating  is  rather 
coarse.  If  we  allow  light  to  pass  through  these  intervals, 
each  interval  may  be  considered  to  act  as  a  source  of  light. 


120 


Light  Waves  and  Their  Uses 


From  each  of  these  sources  it  is  spread  out  in  circular  waves. 
If  the  incident  wave  is  plane  and  falls  normally  upon  the 
grating,  all  these  waves  start  from  the  separate  openings  in 
the  same  phase  of  vibration.  Hence,  in  a  plane  parallel  to 
the  grating  we  should  have,  as  the  resultant  of  all  these 
waves,  a  plane  wave  traveling  in  the  direction  of  the  normal 
to  the  grating.  When  this  wave  is  concentrated  in  the  focus 
of  a  lens,  it  produces  a  single  bright  line,  which  is  the  image 
of  the  slit  and  is  just  as  though  the  grating  were  not  present. 


FIG.  87 


Suppose  we  consider  another  direction,  say  AC  {Fig.  87). 
We  have  a  spherical  wave,  starting  from  the  point  B, 
another  in  the  same  phase  from  the  point  a,  etc.  Now,  if 
the  direction  AC  is  such  that  the  distance  ah  from  the 
opening  a  to  the  line  through  B  perpendicular  to  ^C  is 
just  one  wave,  then  along  the  line  BC  the  light  from  the 
openings  B  and  (i  differ  in  phase  by  one  whole  wave.  When 
(lb  is  equal  to  one  wave,  cd  will  be  equal  to  two  waves; 
hence,  along  BC  the  light  from  the  opening  c  will  be  one 
wave  behind  the  light  from  a,  etc. ;  and  if  these  waves  are 
brought  to  a  focus,  they  will  produce  a  bright  image  of  the 
source.  Since  the  wave  lengths  are  different  for  different 
colors,  the  direction  AC  in  which  this  condition  is  fulfilled 
will  be  different  for  different  colors.      A  grating  will  there- 


Action  of  Magnetism  on  Light  Waves     121 

fore  sort  out  the  colors  from  a  source  of  light  ind  bend  them 
at  different  angles,  forming  a  spectrum.  Since  the  blue 
waves  are  shorter  than  the  red,  the  blue  will  be  bent  least 
and  the  red  most,  the  intervening  colors  coming  in  their 
proper  order  between.  Again,  we  may  also  have  an  image 
formed  when  the  direction  AC  is  such  that  this  difference 
in  phase  of  the  light  from  successive  openings,  instead  of  one 
wave,  is  two.  The  spectrum  thus  formed  is  said  to  be  of 
the  second  order.  When  this  difference  in  phase  is  three 
waves,  the  spectrum  is  said  to  be  of  the  third  order,  etc. 

Plate  I,  Fig.  2,  represents  the  spectrum  produced  by  a 
coarse  grating.  The  source  of  light  was  a  narrow  slit  illumi- 
nated by  sunlight.  The  central  image  appears  just  as  though 
no  grating  were  present,  and  on  either  side  are  diffuse  spec- 
tral images  colored  as  on  Plate  I.  Three  such  images, 
which  are  the  spectra  of  the  first,  second,  and  third  orders, 
may  be  counted  on  the  right,  and  the  same  on  the  left.  The 
grating  used  in  producing  this  picture  had  about  six  hun- 
dred openings  to  the  inch.  Now,  a  finer  grating  produces  a 
much  greater  separation  of  the  colors.  The  large  concave 
gratings  used  for  the  best  grade  of  spectroscopic  work  pro- 
duce spectra  of  the  first  order  which  are  four  feet  long. 
Those  of  higher  order  are  correspondingly  longer. 

The  efficiency  of  such  gratings  depends  on  the  total  dif- 
ference of  path  in  wave  lengths  between  the  first  wave  and 
the  last.  Thus  in  the  grating  shown  in  Fig.  87  there  will  be, 
in  the  case  of  the  first  spectrum,  as  many  waves  along  ^C  as 
there  are  openings  between  A  and  B.  If  we  call  the  total 
number  of  openings  in  the  grating  n,  then  there  will  be  n 
waves  along  AC.  In  the  second  spectrum,  then,  since  each 
one  of  the  intervals  corresponds  to  two  waves,  the  total 
difference  in  the  path  is  twice  as  great,  so  that  the  number  of 
waves  in  ^O  will  be  2n.  For  the  third  spectrum  the  num- 
ber would  be  3  n,  and  for  the  mth  spectrum  mn. 


122  Light  Waves  and  Their  Uses 

The  efficiency  of  the  grating  depends  on  the  order  m 
of  the  spectrum  and  the  number  7i  of  lines  in  the  grating, 
/.  e.,  on  the  product  of  the  two.  Hitherto  the  efforts  of 
makers  of  gratings  have  been  directed  toward  increasing  n 
as  much  as  possible  by  making  the  total  number  of  lines  in 
the  grating  as  great  as  possible.  It  has  been  found  that  as 
many  as  100,000  lines  can  be  ruled  side  by  side  on  a  metallic 
surface;  but  in  ruling  100,000  lines  it  is  extremely  difficult 


FIG.  88 


to  get  them  in  their  proper  position.  Very  little  attention 
has  as  yet  been  directed  toward  producing  a  spectrum  of  a 
very  high  order.  The  chief  reason  for  this  is  that  the  inten- 
sity of  the  light  in  the  spectra  of  higher  orders  diminishes 
very  rapidly  as  the  order  increases.  The  first  spectrum  is  by 
far  the  brightest;  the  second  has  an  intensity  of  something 
like  one -third  of  the  first,  and  the  succeeding  spectra  are 
still  fainter.  There  have  been,  occasionally,  gratings  in 
which  the  diamond  point  happened  to  rule  in  such  a  way  as 
to  throw  an  abnormal  proportion  of  light  in  one  spectrum. 
Such  are  exceedingly  rare  and  exceedingly  valuable.  It 
seems  to  be  a  matter  of  chance  whether  the  diamond  rules 
such  gratings  or  not.  It  was  with  the  double  purpose  of 
multiplying  the  order  of  the  spectrum,  and  at  the  same  time 
of  throwing  all  the  light  in  one  spectrum,  that  the  instrument 
shown  in  Fis-  S8  was  devised. 


Action  of  Magnetism  on  Light  Waves      123 


The  method  of  reasoning  which  led  to  the  invention  of 
this  instrument  may  be  of  interest.  We  will  suppose  that, 
in  order  to  throw  the  light  in  one  spectrum,  the  diamond 
point  could  be  made  to  rule  a  grating  with  a  section  like  that 
shown  in  Fig.  89,  the  distance  between  the  steps  being  exactly 
equal  and  the  sur- 
faces of  the  grooves 
perfectly  polished. 
Suppose  that  the  light 
came  in  the  direction 
indicated  nearly  nor- 
mal to  the  surface  of 
the  groove.  The  light 
would  be  reflected 
back  in  the  opposite 
direction,  and  that 
which  came  from  each 
successive  groove 
would  differ  in  phase  from  that  from  the  adjacent  grooves 
by  a  number  of  waves  corresponding  to  double  the  difference 
in  path.  The  retardation,  instead  of  being  one  wave,  would 
be  twice  the  number  of  waves  in  this  distance.  If  the  dis- 
tance between  the  grooves  were  very  large,  the  number  of 
waves  in  this  distance  would  also  be  very  large,  so  that  the 
order  of  the  resulting  spectrum  would  be  correspondingly 
high.  Further,  al^nost  all  the  light  returns  in  one  direction, 
so  that  the  spectrum  we  are  using  will  be  as  bright  as  possible. 

We  have  thus  shown,  at  least  theoretically,  the  possi- 
bility of  producing  a  very  high  order  of  spectrum,  and  at  the 
same  time  of  getting  almost  all  the  light  in  one  spectrum. 
However,  the  necessary  condition  is  that  the  distances 
between  the  grooves  be  equal  within  a  very  small  fraction 
of  a  light  wave.  This  is  a  difficult,  but  not  a  hopeless, 
problem.     In  fact,  we  may  obtain  the  desired  retardation 


FIG.  89 


124  Light  Waves  and  Theie  Uses 

by  piling  up  plates  of  glass  of  the  same  thickness.  These 
plates  of  glass  can  be  made  originally  of  a  single  piece,  as 
nearly  uniform  in  thickness  as  possible.  It  has  been  possible 
to  obtain  plates,  plane  parallel,  so  accurate  that  the  thickness 
was  the  same  all  over  to  within  one-hundredth  of  a  liffht 
wave;  that  is,  less  than  one  five-millionth  of  an  inch.  If 
we  could  place  a  number  of  such  plates  in  contact  with  each 
other,  we  should  have  the  means  of  producing  any  desired 
retardation  of  light  reflected  from  one  surface  over  the  light 
reflected  from  the  next  nearest  surface,  and  should  be  able  to 
make  this  retardation  exactly  the  same  number  of  waves  for 
all  the  intervals.  The  difficulty  lies  in  the  fact  that  we  can- 
not place  the  plates  in  contact  even  by  applying  a  pressure 
large  enough  to  distort  the  glasses,  because  of  dust  particles. 
The  thickness  of  such  particles  is  of  the  order  of  a  light 
wave.  It  is  therefore  difficult  to  get  the  plates  much  closer 
together  than  about  three  waves.  If  this  distance  were 
constant,  no  harm  would  be  done,  but  it  varies  in  different 
cases ;  so  the  extreme  accuracy  of  the  thickness  of  the  glass 
is  practically  valueless. 

Fortunately  there  is  a  way  of  getting  around  the  diffi- 
culty, and  this  way  has,  at  the  same  time,  other  advantages. 
Suppose  that,  instead  of  reflecting  the  light  from  such  a  pile 
of  glass  plates,  we  allow  it  to  go  through.  The  light  travels 
more  slowly  in  glass  than  in  air — in  the  ratio  of  one  and  one- 
half  to  one  —  and  the  retardations  produced  by  the  successive 
plates  in  the  light  which  has  passed  through  are  now  exactly 
the  same.  In  this  way  it  has  been  found  possible  to  utilize  as 
many  as  twenty  or  thirty  of  such  plates,  and  the  retardation 
produced  by  each  plate  would  correspond  to  the  difference  in 
the  optical  path  between  a  layer  of  air  and  an  equally  thick 
layer  of  glass.  Some  of  these  plates  have  been  made  as 
thick  as  one  inch.  Roughly  speaking,  there  are  50,000 
waves  in  an  inch  of  air ;  the  number  in  an  equal  thickness  of 


Action  of  Magnetism  on  Light  Waves      125 

glass  would  be  one  and  one-half  times  as  great,  so  that  the 
difference  in  path  would  be^25,000  waves.  But  the  resolving 
power  is  the  order  of  spectrum  multiplied  by  the  number  of 
plates.  If  we  are  observing,  therefore,  in  the  25,000th 
spectrum,  and  there  are  thirty  such  plates,  the  resolving  power 
would  be  750,000;  whereas  the  resolving  power  of  the  best 
gratings  is  about  100,000. 

There  are,  however,  disadvantages  in  the  use  of  this  in- 
strument. One  of  these  may  be  illustrated  as  follows:  Sup- 
pose we  take  the  case  of  the  ordinary  grating;  the  first 
spectral  image  is  rather  widely  separated  from  the  central 
image  of  the  slit,  the  second  spectral  image  is  twice  as  far 
away  as  the  first,  and  the  third  spectral  image  will  start 
three  times  as  far  away  as  the  first,  and  will  also  be  three 
times  as  long.  The  result  is  that  parts  of  the  second  and 
third  overlap.  The  overlapping  becomes  greater  and  greater 
as  the  order  of  the  spectrum  increases,  so  that  when  the 
25,000th  spectrum  is  reached  the  spectra  are  inextricably 
confused.  Where  we  have  to  deal  with  a  few  simple  radia- 
tions, however,  as  in  cadmium  or  sodium,  this  overlapping  is 
not  so  serious  as  might  be  supposed.  We  have  a  very 
simple  means  of  getting  rid  of  the  worst  of  it  by  analyzing 
the  light  by  means  of  a  prism  before  it  enters  the  pile  of 
plates. 

The  construction  of  the  instrument  is  not  very  different 
from  that  of  the  ordinary  spectroscope.  The  light  passes 
through  a  slit  and  then  through  a  lens,  by  which  it  is  made 
parallel.  It  then  passes  through  the  pile  of  plates — the 
echelon,  as  it  has  been  named — and  into  the  observing  tele- 
scope. With  this  instrument  the  results  obtained  by  the 
method  of  visibility  curves  have  been  confirmed.  Thus  Fig. 
81  shows  the  appearance  of  the  green  mercury  line  in  the 
field  of  view  of  the  echelon  when  the  source  is  in  a  strong 
magnetic  field.     In  the  three  central  components  the  vibra- 


126  Light  Waves  and  Their  Uses 

tions  are  horizontal,  while  in  the  outer  three  on  both  sides 
the  vibrations  are  vertical.  An  idea  of  the  power  of  this 
instrument  can  be  obtained  by  comparing  Fig.  81  with  Fig. 
80,  which  gives  the  appearance  of  the  line  as  seen  in  the  best 
grating  spectroscope. 

SUMMARY 

1.  The  investigation  of  the  changes  produced  in  the  radia- 
tions of  substances  by  placing  them  in  the  magnetic  field  is  in 
general  a  phenomenon  barely  within  the  range  of  the  best 
spectroscopes,  and  there  are  some  features  of  it  which  it 
would  be  entirely  hopeless  to  attack  by  this  method. 

2.  Such  investigations,  however,  are  precisely  the  kind 
for  which  the  interference  method  is  particularly  adapted. 
In  fact,  the  results  of  the  investigation  by  the  method  of 
visibility  curves  have  furnished  a  number  of  new  and  interest- 
ing developments  which  could  only  with  difficulty  have  been 
obtained  by  the  ordinary  spectrometer  methods. 

3.  Fertile  as  this  method  has  shown  itself  to  be,  there  are, 
nevertheless,  a  number  of  serious  drawbacks.  In  order  to 
obviate  these  a  new  instrument  was  devised,  the  echelon 
spectroscope,  which  has  all  the  advantages  of  the  grating  spec- 
troscope, together  with  a  resolving  power  many  times  as  great. 
With  the  aid  of  this  instrument  all  the  preceding  deductions 
have  been  amply  verified  and  a  number  of  new  and  interest- 
ing facts  added  to  the  store  of  our  knowledge  of  the  Zeeman 
effect. 


LECTURE  VII 

APPLICATION    OF    INTERFERENCE     METHODS    TO 
ASTRONOMY 

Our  knowledge  of  the  heavenly  bodies  is  still  very  limited. 
The  little  that  we  have  learned  has  been  acquired  almost  en- 
tirely with  the  assistance  of  the  telescope,  or  the  telescope 
compounded  with  the  spectroscope.  Without  these,  the  stars 
and  the  planets  would  always  remain,  even  to  the  most 
perfect  unaided  vision,  as  simple  points  of  light.  With 
these  aids  we  are  every  year  adding  very  much  to  our  knowl- 
edge of  their  constitution,  their  form,  their  structure,  and  their 
motions.  For  example,  the  spectroscope  gives  information 
concerning  the  elements  contained  in  the  sun  and  the  stars; 
for  by  means  of  the  dark  or  bright  lines  in  the  spectrum  we 
are  able  to  identify  elements  by  the  position  of  their  spec- 
tral lines,  and  from  this  identification  we  are  able  to  infer, 
with  almost  absolute  certainty,  the  presence  of  the  corre- 
sponding material  in  the  heavenly  body  which  is  examined. 
The  same  is  true  of  comets  and  nebulae.  By  the  general 
character  of  the  spectrum  we  may  also  distinguish  whether 
these  bodies  are  in  the  form  of  incandescent  gases,  or 
whether  they  are  in  solid  or  liquid  form;  and  we  can,  to  a 
certain  extent,  infer  their  temperature.  We  can  even  deter- 
mine whether  the  body  is  approaching  or  receding.  For 
example,  if  the  body  is  approaching,  the  waves  are  crowded 
together  so  that  their  wave  length  will  be  shortened,  and 
hence  they  have  a  correspondingly  altered  position  in  the 
spectrum,  l.  e.,  the  line  will  be  shifted  toward  the  blue  end 
of  the  spectrum.  If  the  body  is  receding,  the  spectral  line 
is  shifted  in  position  toward  the  red  end  of  the  spectrum. 

127 


128  Light  Waves  and  Theik  Uses 


By  the  telescope  we  have  discovered  that  all  the  planets, 
including  many  of  the  minor  planets,  have  discs  of  appre- 
ciable size.  We  have  found  markings  on  the  planets,  have 
discovered  the  satellites  of  Jupiter  and  the  rings  of  Saturn, 
and  have  observed  various  interesting  details  concerning  the 
structure  of  these  rings.  The  strange  markings  on  the 
planet  Mars,  which  bear  such  a  remarkable  resemblance  to 
the  works  of  intelligent  beings,  are  among  the  most  interest- 
ing of  the  recent  revelations  of  the  telescope. 

It  is  hard  to  realize  that  such  observations  concern 
bodies  that  are  distant  millions  of  miles  from  us;  in  fact, 
the  distance  is  so  great  that  it  can  be  more  readily  ex- 
pressed by  the  time  light  takes  to  reach  us  from  these 
bodies.  In  some  cases  this  may  be  as  much  as  several 
years.  We  can  compare  this  distance  with  the  circumference 
of  the  earth,  by  considering  that  light  or  a  telegram  will 
go  around  the  earth  seven  times  in  a  second,  while  from 
these  bodies  it  would  take  several  hours  for  light  to  reach  us. 
Yet  these  are  our  nearest  neighbors,  or,  rather,  members  of 
our  immediate  family.  Our  farther  neighbors  are  so  remote 
that  probably  the  light  from  many  of  them  has  not  yet 
reached  us.  To  these  more  distant  bodies  our  own  little 
family  of  planets  is  probably  invisible;  even  the  sun  itself 
is  a  second-rate  star.  If,  however,  Jupiter  were  sufficiently 
bright,  then  the  sun  and  Jupiter  together  would  form  what 
is  called  a  "  double  star,"  and  to  an  inhabitant  of  a  distant 
planet  which  might  be  traveling  about  this  distant  star  it 
would  appear  as  a  double  star  with  a  separation  of  about  one 
second,  which  may  be  expressed  as  the  angle  subtended  by 
two  luminous  points  about  one-half  inch  apart  when  at  a 
distance  of  three  miles.  They  would  therefore  be  entirely 
invisible  to  the  naked  eye  as  separate  objects. 

One  of  the  most  serious  difficulties  in  the  way  of  further 
progress  in  the  investigation  of  the  telescopic  characteristics 


Interference  Methods  in  Astronomy      129 

of  the  planets  and  of  the  constitution  of  star  systems,  is  what 
is  called  bad  "  seeing."  It  must  be  remembered  that  light,  in 
order  to  reach  a  telescope,  must  pass  through  from  forty  to 
one  hundred  miles  of  atmosphere.  This  atmosphere  is  not 
homogeneous.  If  the  atmosphere  were  homogeneous,  there 
would  not  be  any  very  serious  objection.  The  intensity  of  the 
light  from  the  object  would  be  practically  as  great  as  if  there 
were  no  air  present.  But  the  air  is  unequally  heated,  and 
therefore  has  unequal  densities  in  difPerent  portions.  Hence 
the  different  portions  of  a  beam  of  light  which  have  passed 
through  different  parts  of  the  atmosphere  and  reached 
different  parts  of  the  objective  of  the  telescope  would  be 
differently  retarded,  and  these  differences  in  retardation 
would  not  be  constant,  but  would  vary,  sometimes  rapidly 
and  sometimes  slowly,  producing  what  is  technically  called 
"  boiling." 

This  unsteadiness  of  the  image  is  the  most  serious  diffi- 
culty with  which  astronomers  have  to  contend;  there  is  no 
instrumental  remedy.  The  best  that  can  be  done  is  to 
choose  an  appropriate  site,  and  it  seems  to  be  the  general 
opinion  of  astronomers  that  such  a  site  is  best  chosen  on 
some  very  high  plateau  or  tableland.  By  some  it  is  con- 
sidered that  a  high  mountain  top  is  a  desirable  location,  and 
there  is  no  question  that  such  a  site  possesses  very  marked 
advantages  in  consequence  of  the  rarity  of  the  air.  If  the 
air  were  very  rare,  "boiling"  would  have  less  effect  than 
it  has  in  dense  air.  But  to  compensate  this  advantage  we 
have  the  very  bad  effect  of  currents  of  heated  air  traveling 
up  the  side  of  the  mountain.  As  a  matter  of  fact,  however, 
even  in  the  worst  locations,  there  are  occasional  nights  when 
the  astronomer  has  almost  perfect  seeing  —  when  even  the 
largest  instruments  attain  almost  their  theoretical  limit  of 
accuracy.  This  theoretical  efficiency  may  be  most  con- 
veniently tested  by  observations  on  double  stars. 


130 


Light  Waves  and  Their  Uses 


being  Ti)  wi) 
angle  would  be 


The  resolving  power,  as  shown  in  one  of  the  preced- 
ing lectures,  depends  on  the  size  of  the  diffraction  rings 
which  are  produced  about  the  image  of  a  star.  It  was  also 
shown  that  the  smallest  angle  which  a  telescope  could 
resolve  was  that  subtended  at  the  center  of  the  lens  by  the 

radius  of  the  first  dark  ring, 
and  this  angle  is  equal  to  the 
ratio  of  the  length  of  the  light 
wave  to  the  diameter  of  the 
objective.  For  example,  if 
we  consider  a  4-inch  glass, 
the  length  of  the  light  wave 
i —  of  an  inch,  this 
^i If 

3  0  0  0  0  0-         ^^ 

the  lens  were  a  40-inch  glass, 
the  angle  would  be  something 
like  3  Q  Q^  QQ  Q,  which  can  be 
represented  by  the  angle  sub- 
tended by  a  dime  at  the  distance  of  fifteen  miles.      Hence,  if 
we  had  two  such  dimes  placed  side  by  side,  the  largest  glass 
would  scarcely  separate  them. 

Fig.  90  is  an  actual  photograph  of  the  image  of  a  point 
of  light  taken  with  an  aperture  smaller  than  that  of  a  tele- 
scope, but  otherwise  under  the  same  conditions  under  which 
a  telescope  is  used.  It  is  easy  to  see  that,  surrounding  the 
point  of  the  image,  there  is  a  more  or  less  defined  white 
disc,  and  beyond  this  a  dark  ring.  Outside  of  this  dark  ring 
there  are  a  bright  ring  and  another  dark  ring.  Theoretically, 
there  are  a  great  number  of  those  rings;  practically,  we  see 
only  one  or  two  under  the  most  favorable  conditions. 

This  figure  represents  the  appearance  of  the  image  of  one 
of  Jupiter's  satellites  as  it  would  be  observed  in  one  of  the 
largest  telescopes  under  the  most  favorable  conditions.  If 
it  be  required  to  measure  the  diameter  of  one  of  these  very 


FIG.  90 


Intebference  Methods  in  Astronomy       131 


FIG.  91 


distant  objects,  a  pair  of  parallel  wires  is  placed  as  nearly  as 
possible  upon  what  is  usually  called  the  edge  of  the  disc,  as 
shown  in  Fig.  91.  The  position 
of  this  edge  varies  enormously 
with  the  observer.  One  observer 
will  suppose  it  well  within  the 
white  portion;  another,  on  the 
edge  of  the  black  portion.  Then, 
too,  the  images  vary  with  atmos- 
pheric conditions.  In  the  case 
of  an  object  relatively  distinct 
there  may  be  an  error  of  as  much 
as  5  to  10  per  cent.  In  many 
cases  we  are  liable  to  an  error 
which  may  amount  to  15  per 
cent.,  while  in  some  measurements  there  are  errors  of  20 
to  30  per  cent. 

Suppose  the  object  viewed  were  a  double  star.  In 
general,  the  appearance  would  be  very  much  like  that  repre- 
sented in  Fig.  92,  except  that,  as  before  stated,  in  the  actual 

case  the  appearance  %ould  be 
troubled  by  "boiling."  It  will 
be  noted  that  as  long  as  the 
diffraction  rings  are  well  clear 
of  each  other  we  need  not  have 
the  slightest  hesitation  in  say- 
ing that  the  object  viewed  is  a 
double  star. 

Fig.  93  represents  under  ex- 
actly the  same  conditions  two 
points,  artificial  double  stars, 
but  very  much  closer  together. 
In  this  case  the  diffraction  rings  overlap  each  other.  It 
will  be  seen  that  the  central  spot  is  elongated,  and  the  expert 


## 


FIG.  92 


132 


Light  Waves  and  Their  Uses 


FIG.  93 


astronomer  may  decide  that  the  star  is  double.     This  elon- 
gation can  under  favorable  circumstances  be  detected  even  a 

considerable  time  after  the 
diffraction  rings  merge  into 
each  other.  If  the  atmospheric 
conditions  were  a  little  worse, 
such  a  close  double  would  be 
indistinguishable  from  the 
single  star,  and  if  the  stars 
were  a  little  closer  together, 
it  would  be  practically  impos- 
sible to  separate  them. 

Fig.  94  represents  the  case 
of  a  triple  star  whose  compo- 
nents are  so  close  together  as  to  be  barely  within  the  limit  of 
resolution  of  the  telescope.  In  this  case  the  object  would 
probably  be  taken  as  triple  because  its  central  portion  is  trian- 
gular. If  the  three  stars  were  a  little  closer  together,  it 
would  be  impossible  to  say  whether  the  object  viewed  were  a 
single  or  a  double  star,  or  a  triple 
star,  or  a  circular  disc. 

If  now,  in  measuring  the 
distance  between  two  double 
stars,  or  the  diameter  of  a  disc 
such  as  that  presented  by  a 
small  satellite  or  one  of  the 
minor  planets,  instead  of  at- 
tempting to  measure  what  is 
usually  called  the  "edge"  of 
the  disc  —  which,  as  before 
stated,  is  a  very  uncertain  thing 
and  varies  with  the  observer  and 
with  atmospheric  conditions  —  we  try  to  find  a  relation  be- 
tween the  size  and  shape  of  the  object  and  the  clearness  of 


FIG.  94 


Interference  Methods  in  Astronomy   133 


FIG.  95 


the  interference  fringes,  we  should  have  a  means  of  making 
an  independent  measurement  of  the  size  of  objects  which  are 
practically  beyond  the  power  of  resolution  of  the  most  power- 
ful telescope.  The  principal  object  of  this  lecture  is  to  show 
the  feasibility  of  such  methods  of  measurement.  For  this 
purpose,  however,  the  circular 
fringes  that  we  have  been  in- 
vestigating are  not  very  well 
adapted;  they  are  not  very 
sharply  defined;  there  is  not 
enough  contrast  between  them. 
However,  there  is  a  relation 
which  can  be  traced  oat  be- 
tween the  clearness  of  the  dif- 
fraction fringes  and  the  size 
and  shape  of  the  object  viewed. 
This  relation  is  very  complex. 

The  result  of  such  calculation  is  that  the  intensity  is 
greatest  at  the  center,  whence  it  rapidly  falls  off  to  zero  at 
the  first  dark  band.  It  then  increases  to  a  second  maxi- 
mum, where  it  is  not  more  than  one-ninth  as  great  as  in 
the  center.  What  we  should  have  to  observe,  then,  is  the 
contrast  between  these  two  parts — one  but  one-ninth  as 
marked  as  the  other  and  confused  more  or  less  by  atmos- 
pheric disturbances.  In  case  of  a  rectangular  aperture  the 
intensity  curve  is  somewhat  different,  in  that  the  maxima 
on  either  side  of  the  central  band  are  considerably  greater, 
so  that  it  is  somewhat  easier  to  see  the  fringes.  In  case 
of  the  rectangular  aperture  the  fringes  are  parallel  to  the 
long  sides  of  the  rectangle.  The  appearance  of  the  dif- 
fraction phenomenon  in  this  case  is  illustrated  in  Fig. 
95.  The  pattern  consists  of  a  broad  central  space,  whose 
sides  are  parallel  to  the  sides  of  the  rectangular  slit,  and 
of    a    succession    of    fringes    diminishing    in    intensity    on 


134 


Light  Waves  and  Their  Uses 


FIG.  96 


either  side.      The   corresponding    intensity  curve  is   shown 
in  Fig.  96.' 

If  we  had  two  such  apertures  instead  of  one,  the  ap- 
pearance would  be  all  the  more 
definite;  but  the  two  apertures  to- 
gether produce,  in  addition,  inter- 
ference fringes  very  much  finer 
than  the  others,  but  very  sharp 
and  clear.  The  intensity  curve  cor- 
responding to  these  two  slits  is  shown  in  Fig.  97.  In  this 
case  it  is  easy  to  distinguish  the  successive  maxima,  and  the 
atmospheric  disturbances  are  very  much  less  harmful  than 
in  the  case  of  the  more  indefinite  phenomenon. 

Fig.  98  represents  the  appearance  of  the  diffraction  pat- 
tern due  to  two  slits  when  a  slit,  instead  of  a  point,  is  used 
as  the  source  of  light.  The  appearance  of  the  two  patterns 
is  not  essentially  different,  that  due  to  the  slit  being  very 
much  brighter.  In  the  case  of  a  point  source  there  is  so 
little  light  that  it  is  more  difficult  to  see  the  fringes.  Here 
the  same  large  fringes  are  visible  as  before,  but  over  the 
central  bright  space  there  is  a  number  of  very  fine  fringes. 
The  two  central  ones  are  particularly  sharp,  so  that  it  is 
easy  to  locate  their  position  if  necessary,  but  still  easier  to 
determine  their  visibility.  This  clearness 
is  the  essential  point  we  have  to  consider, 
because  the  size  of  the  object  determines 
the  clearness  of  the  fringes.  We  find  that 
if  we  gradually  increase  the  width  of  the 
source,  the  fringes  grow  less  and  less  dis- 
tinct, and  finally  disappear  entirely.  If 
wo  note  the  instant  when  the  fringes  disappear,  we  can  calcu- 
late from  the  dimensions  of  the  apparatus  the  width  of  the 


FIG.  97 


'This  ifjnores  tho  diffraction  bands  parallel  to  the  shorter  sides  of  the  rect- 
angle, which  are  usually  iuconsijicuous. 


Inteefeeence  Methods  in  Asteonomy        135 


source.  Or,  if  we  alter  the  dimensions  of  the  apparatus 
and  observe  when  the  fringes  cease  to  be  visible  in  onr 
observing  telescope,  we  have  the  means  of  measuring  the 
diameter  of  the  source,  which  may  be  a  double  star,  or  the 
disc  of  one  of  Jupiter's  satellites,  or  one  of  the  minor  planets. 

We  may  get  some  notion 
of  the  relation  which  exists 
between  the  clearness  of  the 
fringes  and  the  size  of  the  ob- 
ject when  the  fringes  disap- 
pear, by  considering  a  simple 
case  like  that  of  a  double  star. 
Suppose  we  have  two  slits  in 
front  of  the  object  glass  of  a 
telescope  focused  on  a  single 
star.  At  the  focus  the  rays 
from  the  two  slits  come  to- 
gether in  condition  to  produce 
interference  fringes,  and  the  fringes  always  appear  when  the 
source  is  a  point.  Suppose  we  have  in  the  field  of  view 
another  star.  It  will  produce  its  own  series  of  fringes  in  the 
focus  of  the  telescope.  We  shall  then  have  two  similar  sets 
of  fringes  in  the  field  of  view.  If,  now,  the  two  stars  are 
so  near  together  that  the  central  bright  fringes  of  the 
two  systems  coincide,  then  the  two  sets  of  fringes  will 
reinforce  each  other.  If,  however,  one  of  the  stars  is  just 
so  far  away  from  the  other  that  the  angle  between  them 
is  equal  to  the  angle  between  the  central  bright  band  and 
its  first  adjacent  minimum,  then  the  maximum  of  one  sys- 
tem of  fringes  will  fall  upon  the  minimum  of  the  other  set, 
and  the  two  will  efface  each  other  so  that  the  fringes  dis- 
appear. Hence  the  fringes  disappear  when  the  angle  sub- 
tended by  the  source  is  equal  to  the  angle  subtended  by 
half    the   breadth   of    the   fringes,  viewed  from  the    objec- 


FIG.  98 


136  Light  Waves  and  Their  Uses 

tive.  This  angle  is  easily  calculated.  Thus  if  I  represent  the 
wave  length  and  s  is  the  distance  between  the  two  slits,  then 

the  angle  is  equal  to  ^  •  -  .     Hence,  if  we  know  the  length 

of  the  light  wave  (we  can  take  it  as  one  fifty-thousandth  of 
an  inch  if  we  choose) ,  by  measuring  the  distance  between 
our  slits  when  the  fringes  disappear  we  have  the  means  of 
measuring  the  angular  distance  between  double  stars. 

In  the  case  of  a  single-slit  source  we  can  also  get  some 
sort  of  an  idea  of  the  conditions  which  prevail  when  the 
fringes  disappear.  For  we  may  conceive  the  slit  source  to 
be  divided  into  a  number  of  line  sources,  parallel  and 
adjacent  to  each  other.  Then  each  line  source  would  form 
its  own  set  of  fringes,  and  when  the  angle  between  the  two 
outside  lines,  i.  e.,  the  edges  of  the  slit,  is  equal  to  the  angle 
subtended  by  the  distance  of  the  first  dark  band  from  the 
center,  the  fringes  again  overlap  in  such  a  way  as  to  dis- 
appear.    The  value  of  this  angle  is  easily  found  to  be  -.    So, 

supposing  that  we  had  such  an  object  in  the  heavens  as  a  nar- 
row band  of  light,  we  have  the  means  of  finding  its  width.  If, 
instead  of  a  slit,  we  used  a  circular  opening  as  a  source,  there 
is  a  little  more  difficulty  in  the  mathematical  analysis.     In  this 

case  the  coefficient  of   -  ,  instead  of  beins^  1  as  in  the  second 

s  ^ 

case,  or  ^  as  in  the  first  case,  is  found  to  be  1.22.  In  observ- 
ing such  an  object  we  measure  the  distance  between  our  two 
slits  when  the  interference  fringes  have  just  vanished,  and 
compute  the  angular  magnitude  of  the  object  by  using  this 
coefficient.  If  we  knew  the  distance  to  the  object,  we  could 
calculate  also  its  actual  diameter. 

The  curve  representing  the  clearness  of  the  fringes  as  the 
slits  approach  is  rather  interesting.      It  varies  with  the  form 


Inteeference  Methods  in  Astronomy   137 

of  the  object  viewed.  In  the  case  of  a  double  star  it  falls  very 
rapidly  from  its  maximum  to  zero ;  then  it  rises  again,  and  if 
the  two  slits  themselves  could  possibly  be  infinitely  narrow 
and  the  light  perfectly  homogeneous,  it  would  rise  to  its  origi- 
nal value.  But  because  the  slits  themselves  have  a  certain 
width,  and  because  the  observation  is  usually  made  with  white 
light,  this  second  maximum  is  usually  less  than  the  first. 

If  the  source  is  a  single  point  of  light,  then  the  fringes 
are  equally  distinct,  no  matter  what  the  distance  between  the 
slits;  whereas,  when  the  source  is  a  disc  of  appreciable 
angular  width,  the  fringes  fade  out  as  the  distance  between 
the  slits  increases,  so  that  there  is  no  possibility  of  a  doubt 
as  to  whether  we  are  looking  at  a  point  or  a  source  of  appre- 
ciable size. 

Suppose  we  are  looking  at  a  disc  of  a  given  diameter 
through  such  a  pair  of  slits  which  are  close  together.  If 
we  gradually  increase  the  distance  between  the  slits,  the 
visibility  becomes  smaller  and  smaller  until  the  fringes  dis- 
appear entirely.  As  the  distance  between  the  slits  increases 
again,  the  clearness  increases,  and  so  on;  i.  e.,  there  are  sub- 
sequent maxima  and  minima  which  may  be  measured,  if  it  be 
considered  desirable.  It  is  necessary,  however,  to  measure 
this  distance  between  the  two  slits  at  the  time  the  fringes 
first  disappear;  we  may  measure  this  distance  at  the  sub- 
sequent disappearances  if  we  choose,  but  it  is  not  essential, 
for  we  are  able  to,  find  the  diameter  of  the  object  (the 
distance  between  two  objects  in  the  case  of  the  double  star) 
if  we  know  the  distance  between  the  slits  at  the  first  dis- 
appearance. If,  however,  we  do  not  know  the  shape  of  the 
source,  we  must  observe  at  least  one  more  disappearance. 

In  Fig.  99  the  visibility  curves  which  characterize  a  slit, 
a  uniformly  illuminated  disc,  and  a  disc  whose  intensity  is 
greater  at  the  center,  are  shown.  The  full  curve  cor- 
responds to  a  slit,  the  dotted  one  to  a  disc,  and  the  dashed 


138 


Light  Waves  and  Their  Uses 


one  to  the  disc  which  is  brighter  at  the  center.  It  will  be 
noted  that  in  the  case  of  the  slit  the  distances  between  the 
zero  points  are  all  alike.  In  the  case  of  the  disc  the  curve 
is  still  of  the  same  general  form,  but  the  distance  to  the  first 
zero  position  is  no  longer  equal  to  the  others,  but  is  1.22  as 
great.  Hence,  if  the  distances  between  the  zero  points  are 
equal,  as  shown  in  the  figure  for  the  full  curve,  we  know  the 


FIG.  99 


source  is  rectangular.  But  if  the  distance  to  the  first  zero 
point  is  1.22  times  as  great  as  the  distances  between  the 
succeeding  zero  points,  we  know  that  we  are  observing  a 
uniformly  illuminated  circular  object.  The  next  interval 
would  determine  in  this  case,  as  in  the  first,  the  diameter  of 
the  object  viewed. 

In  the  case  of  the  slit  the  distances  between  the  zero 
points  are  rigorously  equal,  and  it  may  be  of  interest  to  note 
that  the  visibility  at  the  second  maximum  is  something  like 
one-fourth  of  the  visibility  at  the  first.  So  there  is  no  pos- 
sibility of  deception  in  noting  the  point  at  which  the  fringes 
disappear ;  indeed,  the  disappearance  can  be  so  sharply  deter- 
mined that  we  may  measure  the  corresponding  distance  be- 


Inteeference  Methods  in  Astronomy      139 


tween  the  slits  to  within  1  per  cent,  of  its  whole  value,  and 
so  determine  the  width  of  the  line  source  with  a  corre- 
sponding degree  of  accuracy. 

The  visibility  curve  shown  in  Fig.  100  represents  the  case 
in  which  the  source  is  a  double  disc  —  a  double  star,  for 
instance,  in  which  the 
discs  have  apprecia- 
ble magnitude.  The 
envelope  of  the  curve, 
which  is  drawn  full, 
corresponds  to  the 
circular  form  of  the 
separate  discs,  and 
from  this  curve  we  can 
determine  the  size  of 
the  separate  discs, 
provided  they  are 
equal.  The  dotted 
curve  tells  us  that  we 
are    dealing    with    a 

double  object.  Hence,  if  in  observing  a  heavenly  body  we 
obtain  a  visibility  curve  of  this  form,  we  infer  that  we  are 
dealing  with  a  double  star. 

There  is  a  difficulty  in  carrying  out  such  observations, 
especially  when  we  are  observing  a  very  small  object  or  a 
very  close  double  star.  For  in  this  case  the  slits  have  to  be 
separated  rather  widely,  and  the  angle  between  the  rays 
from  the  two  slits,  when  they  come  together,  is  rather  large. 
Hence,  the  distance  between  the  interference  fringes  is 
correspondingly  small,  as  was  shown  in  a  previous  lecture, 
and  this  distance  becomes  less  and  less  as  the  angle  becomes 
greater  and  greater.  When  we  approach  the  limit  of  reso- 
lution of  the  telescope,  the  fringes  are  so  small  that  a 
rather  high   power  eyepiece   must  be  used  in  order  to  see 


FIG.  100 


140 


Light  Waves  and  Their  Uses 


them,  and  the  light  is  correspondingly  feeble.  We  may  over- 
come this  difficulty  in  the  same  way  as  we  did  in  our  trans- 
formation of  the  microscope  into  the  interferometer,  by  using 
mirrors  to  change  the  direction  of  the  beam  of  light,  instead  of 
allowing  it  to  pass  through  tVo  apertures  in  front  of  the  lens. 
Fig.  101  represents  two  arrangements  by  which  this  may 
be  accomplished.     The  light  falls  from  above  upon  the  two 


FIG.  101 


mirrors  a  and  h,  which  correspond  to  the  two  slits.  By 
these  mirrors  we  can  bend  the  light  at  any  angle  we  choose, 
and  bring  the  two  beams  together  again  at  as  small  an  angle 
as  we  wish,  by  means  of  the  plane-parallel  plate.  Thus  we 
can  make  the  fringes  as  broad  as  we  choose.  In  the  second 
diagram  we  have  a  rather  more  complex  arrangement  of 
mirrors,  but  the  effect  is  the  same.  The  paths  of  the  two 
rays  can  be  easily  traced  in  the  diagrams. 

If  we  wish  to  observe  with  such  an  arrangement  a  body 
of  the  size  of  a  small  satellite,  we  should  have  to  construct 
the  instrument  so  that  the  distance  between  the  two  mirrors 
could  be  altered,  because  these  mirrors  correspond  to  the 


Inteeference  Methods  in  Astronomy      141 

two  slits  whose  distance  apart  must  be  changed.  This  can 
be  done  by  mounting  the  mirror  a  and  the  mirror  6  on  a 
right-  and  left-handed  screw.  On  turning  the  screw  the 
two  mirrors  would  move  in  opposite  directions  through 
equal  distances,  leaving  everything  else  unchanged.  Such 
an  instrument  is  represented  in  Fig.  102.  The  light  falls 
from  below  upon  the  two  mirrors  a  and  h,  which  are 
mounted  on  carriages  which  can  be  moved  in  opposite 
directions  by  the  right-  and  left-handed  screw. 


FIG.  102 

Fig.  103  represents  an  actual  instrument  which  was  used 
in  making  laboratory  experiments  to  test  the  method.  The 
artificial  double  stars,  or  star  discs,  were  pinholes  made  in  a 
sheet  of  platinum.  These  holes  were  as  small  as  it  was  pos- 
sible to  make  them,  of  such  a  diameter  as  to  test  the  resolu- 
tion of  the  telescope,  with  a  bright  source  of  light  behind 
them.  The  left-hand  figure  represents  the  double  slit.  It 
is  mounted  on  a  right-  and  left-handed  screw  and  can  be 
operated  by  the  observer.  The  slits  can  thus  be  moved 
by  a  measurable  quantity,  and  their  distance  apart  when  the 
fringes  disappear  can  be  determined. 

After  making  a  series  of  such  experiments  in  the  labora- 
tory, I  was  invited  to  spend  a  few  weeks  at  the  Lick  Observatory 
at  Mount  Hamilton  to  test  the  method  on  Jupiter's  satellites. 
These  satellites  have  angular  magnitudes  of  something  like 
one  second  of  arc,  so  that  they  should  be  measurable  by  this 


142 


Light  Waves  and  Theik  Uses 


method.  The  actual  micrometric  measurements  which  have 
been  made  of  these  satellites  with  the  largest  telescopes  give 
results  which  vary  considerably  among  themselves.  Hence 
the  interest  in  trying  the  interferometer  method.  The  appa- 
ratus used  was  similar  to  that  shown  in  Fig.  103,  i.  e.,  it 
consisted  of  two  movable  slits  in  front  of  the  objective  of  the 
eleven-inch  glass  at  the  Lick  Observatory. 

The  atmospheric  conditions  at  Mount  Hamilton  while  the 
work  was  in  progress  were  not  altogether  favorable,  so  that 


FIG.  103 


out  of  the  three  weeks'  sojourn  there  there  were  only  four 
nights  which  were  good  enough  to  use,  though  one  of  these 
nights  was  almost  perfect ;  and  on  this  one  night  most  of  the 
measurements  were  made.  The  results  obtained,  together 
with  those  of  four  determinations  which  have  been  made  by 
the  ordinary  micrometer  method,  using  the  largest  telescopes 
available,  are  given  in  the  following  table: 


Number  of  Satellite 

A.  A.  M. 

Eng. 

St. 

Ho. 

Bu. 

I             

1.02 
0.94 
1.37 
1.31 

1.08 
0.91 
1.54 

1.28 

1.02 
0.91 
1.49 

1.27 

1.11 
0.98 
1.78 
1.46 

1.11 

II     

1.00 

Ill 

1.78 

IV  

1.61 

The  numbers  in  the  column  marked  A.  A.  M.  are  the  re- 
sults in  seconds  of  arc  obtained  by  the  interference  method. 
The  other  columns  contain  the  results  obtained  by  the  ordi- 
nary method  by  Engelmann,  Struve,  Hough,  and  Burnham 


Inteefekence  Methods  in  Astronomy   143 

respectively.  The  important  point  to  be  noted  is  that  the 
results  by  the  interference  method  are  near  the  mean  of  the 
other  results,  and  that  the  results  obtained  by  the  other 
method  differ  widely  among  themselves. 

It  is  also  important  to  note  that,  while  an  eleven-inch 
glass  was  used  for  the  observations  by  the  interference 
method,  the  distance  between  the  slits  at  which  the  fringes 
disappear  was  very  much  less  than  eleven  inches;  on  the 
average,  something  like  four  inches.  Now,  with  a  six-inch 
glass  one  can  easily  put  two  slits  at  a  distance  of  four 
inches.  Hence  a  six-inch  glass  can  be  used  with  the  same 
effectiveness  as  the  eleven-inch,  and  gives  results  by  the 
interference  method  which  are  equal  in  accuracy  to  those 
obtained  by  the  largest  telescopes  known.  If  this  same 
method  were  applied  to  the  forty-inch  glass  of  the  Yerkes 
Observatory,  it  would  certainly  be  possible  to  obtain  meas- 
urements of  objects  only  one-sixth  as  large  as  the  satellites 
of  Jupiter. 

The  principal  object  of  the  method  which  has  been 
described  was  not,  however,  to  measure  the  diameter  of  the 
planets  and  satellites,  or  even  of  the  double  stars,  though  it 
seems  likely  now  that  this  will  be  one  rather  important 
object  that  may  be  accomplished  by  it ;  for  some  double  stars 
are  so  close  together  that  it  is  impossible  to  separate  them 
in  the  largest  telescope.  A  more  ambitious  problem,  which 
may  not  be  entirely  hopeless,  is  that  of  measuring  the  diam- 
eter of  the  stars  themselves.  The  nearest  of  these  stars,  as 
before  stated,  is  so  far  away  that  it  takes  several  years 
for  light  from  it  to  reach  us.  They  are  about  100,000 
times  as  far  away  as  the  sun.  If  they  were  as  large  as  the 
sun,  the  angle  they  would  subtend  would  be  about  one- 
hundredth  of  a  second.  A  forty-inch  telescope  can  resolve 
angles  of  approximately  one-tenth  of  a  second,  so  that,  if  we 
were  to  attempt  to  measure,  or  to  observe,  a  disc  of  only 


144  Light  Waves  and  Theie  Uses 

one -hundredth  of  a  second,  it  would  require  an  objective 
whose  diameter  is  o£  the  order  of  forty  feet  — which,  of 
course,  is  out  of  the  question.  It  is,  however,  not  altogether 
out  of  the  question  to  construct  an  interference  apparatus 
such  that  the  distance  between  its  mirrors  would  be  of  this 
order  of  magnitude. 

But  it  is  not  altogether  improbable  that  even  some  of 
the  nearer  stars  are  considerably  larger  than  the  sun,  and  in 
that  case  the  angle  which  they  subtend  would  be  consider- 
ably larger.  Hence  it  might  not  be  necessary  to  have  an 
instrument  with  mirrors  forty  feet  apart.  In  addition  it 
may  be  noted  that  it  is  not  absolutely  necessary  to  observe 
the  disappearance  of  the  fringes  in  order  to  show  that 
the  object  has  definite  magnitude ;  for  if  the  visibility  of  the 
fringes  varies  at  all,  we  know  that  the  source  is  not  a  point. 
For,  suppose  we  observe  the  visibility  curve  of  a  star  which 
is  so  far  away  that  we  know  it  has  no  appreciable  disc.  The 
visibility  curve  would  correspond  to  a  straight  line.  There 
would  be  no  appreciable  difference  in  distinction  of  fringes 
as  the  distance  between  the  slits  was  increased  indefinitely. 
If  we  now  observe  a  star  which  has  a  diameter  of  one- 
hundredth  of  a  second,  we  need  only  to  observe  that  the 
visibility  for  a  large  distance  between  the  slits  is  less  than  in 
the  case  of  the  distant  star,  in  order  to  know  that  the  second 
object  has  an  appreciable  disc,  even  if  the  instruments  were 
not  large  enough  to  increase  the  distance  sufficiently  to 
make  the  fringes  disappear.  From  the  difference  between 
two  such  visibility  curves  we  might  calculate  rather  roughly 
the  actual  magnitude  of  the  stars. 

SUMMARY 

1.  The  investigation  of  the  size  and  structure  of  the 
heavenly  bodies  is  limited  by  the  resolving  power  of  the 
observing  telescope.     When  the  bodies  are  so  small  or  so 


Intekfeeence  Methods  in  Astkonomy     145 

distant  that  this  limit  of  resolution  is  passed,  the  telescope 
can  give  no  information  concerning  them. 

2.  But  an  observation  of  the  visibility  curves  of  the 
interference  fringes  due  to  such  sources,  when  made  by  the 
method  of  the  double  slit  or  its  equivalent,  and  properly 
interpreted,  gives  information  concerning  the  size,  shape,  and 
distribution  of  the  components  of  the  system.  Even  in  the 
case  of  a  fixed  star,  which  may  subtend  an  angle  of  less  than 
one-hundredth  of  a  second,  it  may  not  be  an  entirely  hope- 
less task  to  attempt  to  measure  its  diameter  by  this  means. 


LECTURE   VIII 

THE  ETHER 

The  velocity  of  light  is  so  enormously  greater  than  any- 
thing with  which  we  are  accustomed  to  deal  that  the  mind 
has  some  little  difficulty  in  grasping  it.  A  bullet  travels  at 
the  rate  of  approximately  half  a  mile  a  second.  Sound,  in  a 
steel  wire,  travels  at  the  rate  of  three  miles  a  second.  From 
this — if  we  agree  to  except  the  velocities  of  the  heavenly 
bodies  —  there  is  no  intermediate  step  to  the  velocity  of 
light,  which  is  about  186,000  miles  a  second.  We  can,  per- 
haps, give  a  better  idea  of  this  velocity  by  saying  that  light 
will  travel  around  the  world  seven  times  between  two  ticks 
of  a  clock. 

Now,  the  velocity  of  wave  propagation  can  be  seen,  with- 
out the  aid  of  any  mathematical  analysis,  to  depend  on  the 
elasticity  of  the  medium  and  its  density;  for  we  can  see 
that  if  a  medium  is  highly  elastic  the  disturbance  would  be 
propagated  at  a  great  speed.  Also,  if  the  medium  is  dense 
the  propagation  would  be  slower  than  if  it  were  rare.  It 
can  easily  be  shown  that  if  the  elasticity  were  represented  by 
E,  and  the  density  by  D,  the  velocity  would  be  represented 
by  the  square  root  of  E  divided  by  D.  So  that,  if  the  den- 
sity of  the  medium  which  propagates  light  waves  were  as 
great  as  the  density  of  steel,  the  elasticity,  since  the  velocity 
of  light  is  some  60,000  times  as  great  as  that  of  the  propa- 
gation of  sound  in  a  steel  wire,  must  be  60,000  squared 
times  as  great  as  the  elasticity  of  steel.  Thus,  this  medium 
which  propagates  light  vibrations  would  have  to  have  an 
elasticity  of  the  order  of  3,600,000,000  times  the  elasticity 
of  steel.     Or,  if  the  elasticity  of  the  medium  were  the  same 

146 


The  Ether  147 


as  that  of  steel,  the  density  would,  have  to  be  3,600,000,000 
times  as  small  as  that  of  steel,  that  is  to  say,  roughly 
speaking,  about  50,000  times  as  small  as  the  density  of  hydro- 
gen, the  lightest  known  gas.  Evidently,  then,  a  medium 
which  propagates  vibrations  with  such  an  enormous  velocity 
must  have  an  enormously  high  elasticity  or  abnormally  low 
density.  In  any  case,  its  properties  would  be  of  an  entirely 
different  order  from  the  properties  of  the  substances  with 
which  we  are  accustomed  to  deal,  so  that  it  belongs  in  a 
category  by  itself. 

Another  course  of  reasoning  which  leads  to  this  same 
conclusion  —  namely,  that  this  medium  is  not  any  ordinary 
form  of  matter,  such  as  air  or  gas  or  steel  —  is  the  following : 
Sound  is  produced  by  a  bell  under  a  receiver  of  an  air  pump. 
When  the  air  has  the  same  density  inside  the  receiver  as 
outside,  the  sound  reaches  the  ear  of  an  observer  without 
difficulty.  But  when  the  air  is  gradually  pumped  out  of  the 
receiver,  the  sound  becomes  fainter  and  fainter  until  it  ceases 
entirely.  If  the  same  thing  were  true  of  light,  and  we 
exhausted  a  vessel  in  which  a  source  of  light  —  an  incandes- 
cent lamp,  for  example — had  been  placed,  then,  after  a  certain 
degree  of  exhaustion  was  reached,  we  ought  to  see  the  light 
less  clearly  than  before.  We  know,  however,  that  the  con- 
trary is  the  case,  i.  e. ,  that  the  light  is  actually  brighter  and 
clearer  when  the  exhaustion  of  the  receiver  has  been  carried 
to  the  highest  possible  degree.  The  probabilities  are  enor- 
mously against  the  conclusion  that  light  is  transmitted  by 
the  very  small  quantity  of  residual  gas.  There  are  other 
theoretical  reasons,  into  which  we  will  not  enter. 

Whatever  the  process  of  reasoning,  we  are  led  to  the 
same  result.  We  know  that  light  vibrations  are  transverse 
to  the  direction  of  propagation,  while  sound  vibrations  are  in 
the  direction  of  propagation.  We  know  also  that  in  the  case 
of  a  solid  body  transverse  vibrations  can  be  readily  trans- 


148  Light  Waves  and  Their  Uses 

mitted.  Thus,  if  we  have  a  long  cylindrical  rod  and  we  give 
one  end  of  it  a  twist,  the  twist  will  travel  along  from  one  end 
to  the  other.  If  the  medium,  instead  of  being  a  solid  rod, 
were  a  tube  of  liquid,  and  were  twisted  at  one  end,  there 
would  be  no  corresponding  transmission  of  the  twist  to  the 
other  end,  for  a  liquid  cannot  transmit  a  torsional  strain. 
Hence  this  reasoning  leads  to  the  conclusion  that  if  the 
medium  which  propagates  light  vibrations  has  the  proper- 
ties of  ordinary  matter,  it  must  be  considered  to  be  an  elastic 
solid  rather  than  a  fluid. 

This  conclusion  was  considered  one  of  the  most  formi- 
dable objections  to  the  undulatory  theory  that  light  con- 
sists of  waves.  For  this  medium,  notwithstanding  the 
necessity  for  the  assumption  that  it  has  the  properties  of  a 
solid,  must  yet  be  of  such  a  nature  as  to  offer  little  resist- 
ance to  the  motion  of  a  body  through  it.  Take,  for  example, 
the  motion  of  the  planets  around  the  sun.  The  resistance 
of  the  medium  is  so  small  that  the  earth  has  been  travel- 
ing around  the  sun  millions  of  years  without  any  appre- 
ciable increase  in  the  length  of  the  year.  Even  the  vastly 
lighter  and  more  attenuated  comets  return  to  the  same  point 
periodically,  and  the  time  of  such  periodical  returns  has 
been  carefully  noted  from  the  earliest  historical  times,  and 
yet  no  appreciable  increase  in  it  has  been  detected.  We  are 
thus  confronted  with  the  apparent  inconsistency  of  a  solid 
body  which  must  at  the  same  time  possess  in  such  a  marked 
degree  the  properties  of  a  perfect  fluid  as  to  offer  no  appre- 
ciable resistance  to  the  motion  of  bodies  so  very  light  and 
extended  as  the  comets.  We  are,  however,  not  without  analo- 
gies, for,  as  was  stated  in  the  flrst  lecture,  substances  such 
as  shoemaker's  wax  show  the  properties  of  an  elastic  solid 
when  reacting  against  rapid  motions,  but  act  like  a  liquid 
under  pressures. 

In  the  case  of  shoemaker's  wax  both  of  these  contradictory 


The  Ethee  119 


properties  are  very  imperfectly  realized,  but  we  can  argue 
from  this  fact  that  the  medium  which  we  are  considering 
might  have  the  various  properties  which  it  must  possess 
in  an  enormously  exaggerated  degree.  It  is,  at  any  rate, 
not  at  all  inconceivable  that  such  a  medium  should  at  the 
same  time  possess  both  properties.  We  know  that  the  air 
itself  does  not  possess  such  properties,  and  that  no  matter 
which  we  know  possesses  them  in  sufficient  degree  to 
account  for  the  propagation  of  light.  Hence  the  conclusion 
that  light  vibrations  are  not  propagated  by  ordinary  mat- 
ter, but  by  something  else.  Cogent  as  these  three  lines 
of  reasoning  may  be,  it  is  undoubtedly  true  that  they  do  not 
always  carry  conviction.  There  is,  so  far  as  I  am  aware, 
no  process  of  reasoning  upon  this  subject  which  leads 
to  a  result  which  is  free  from  objection  and  absolutely 
conclusive. 

But  these  are  not  the  only  paradoxes  connected  with  the 
medium  which  transmits  light.  There  was  an  observation 
made  by  Bradley  a  great  many  years  ago,  for  quite 
another  purpose.  He  found  that  when  we  observe  the  posi- 
tion of  a  star  by  means  of  the  telescope,  the  star  seems 
shifted  from  its  actual  position,  by  a  certain  small  angle 
called  the  ang^le  of  aberration.  He  attributed  this  effect  to 
the  motion  of  the  earth  in  its  orbit,  and  gave  an  explana- 
tion of  the  phenomenon  which  is  based  on  the  corpus- 
cular theory  and  is  apparently  very  simple.  We  will 
give  this  explanation,  notwithstanding  the  fact  that  we 
know  the  corpuscular  theory  to  be  erroneous. 

Let  us  suppose  a  raindrop  to  be  falling  vertically  and  an 
observer  to  be  carrying,  say,  a  gun,  the  barrel  being  as 
nearly  vertical  as  he  can  hold  it.  If  the  observer  is  not 
moving  and  the  raindrop  falls  in  the  center  of  the  upper 
end  of  the  barrel,  it  will  fall  centrally  through  the  lower 
end.     Suppose,   however,   that    the    observer  is  in    motion 


150 


Light  Waves  and  Their  Uses 


I    1 


n 


in  the  direction  bd  (Fig.  104) ;  the  raindrop  will  still  fall 
exactly  vertically,  but  if  the  gun  advances  laterally  while 
the  raindrop  is  within  the  barrel,  it  strikes  against  the  side. 
In  order  to  make  the  raindrop  move  centrally  along 
the  axis  of  the  barrel,  it  is  evidently  necessary  to 
incline  the  gun  at  an  angle  such  as  bad.  The 
gun  barrel  is  now  pointing,  apparently,  in  the 
wrong  direction,  by  an  angle  whose  tangent  is  the 
ratio  of  the  velocity  of  the  observer  to  the  velocity 
of  the  raindrop. 

According  to  the  undulatory  theory,  the  ex- 
planation is  a  trifle  more  complex;  but  it  can 
easily  be  seen  that,  if  the  medium  we  are  consider- 
ing is  motionless  and  the  gun  barrel  represents  a 
telescope,  and  the  waves  from  the  star  are  moving 
in  the  direction  ad,  they  will  be  concentrated  at  a 
point  which  is  in  the  axis  of  the  telescope,  unless 
the  latter  is  in  motion.  But  if  the  earth  carrying 
the  telescope  is  moving  with  a  velocity  something 
like  twenty  miles  a  second,  and  we  are  observing 
the  stars  in  a  direction  approximately  at  right 
angles  to  the  direction  of  that  motion,  the  light 
from  the  star  will  not  come  to  a  focus  on  the  axis 
of  the  telescope,  but  will  form  an  image  in  a  new 
position,  so  that  the  telescope  appears  to  be  point- 
ing in  the  wrong  direction.  In  order  to  bring  the 
image  on  the  axis  of  the  instrument,  we  must  turn 
the  telescope  from  its  position  through  an  angle 
whose  tangent  is  the  ratio  of  the  velocity  of  the  earth  in  its 
orbit  to  the  velocity  of  light.  The  velocity  of  light  is,  as 
before  stated,  180,000  miles  a  second  —  200,000  in  round 
numbers — and  the  velocity  of  the  earth  in  its  orbit  is  roughly 
twenty  miles  a  second.  Hence  the  tangent  of  the  angle  of 
aberration  would  be  measured  by  the  ratio  of  1  to  10,000. 


FIG.  104 


The  Ether  151 


More  accurately,  this  angle  is  20  f445.  The  limit  of  accuracy 
of  the  telescope,  as  was  pointed  out  in  several  of  the  pre- 
ceding lectures,  is  about  one-tenth  of  a  second;  but,  by 
repeating  these  measurements  under  a  great  many  variations 
in  the  conditions  of  the  problem,  this  limit  may  be  passed, 
and  it  is  practically  certain  that  this  number  is  correct  to  the 
second  decimal  place. 

When  this  variation  in  the  apparent  position  of  the  stars 
was  discovered,  it  was  accounted  for  correctly  by  the  as- 
sumption that  light  travels  with  a  finite  velocity,  and  that, 
by  measuring  the  angle  of  aberration,  and  knowing  the  speed 
of  the  earth  in  its  orbit,  the  velocity  of  light  could  be  found. 
This  velocity  has  since  been  determined  much  more  accu- 
rately by  experimental  means,  so  that  now  we  use  the  velocity 
of  light  to  deduce  the  velocity  of  the  earth  and  the  radius 
of  its  orbit. 

The  objection  to  this  explanation  was,  however,  raised 
that  if  this  angle  were  the  ratio  of  the  velocity  of  the 
earth  in  its  orbit  to  the  velocity  of  light,  and  if  we  filled 
a  telescope  with  water,  in  which  the  velocity  of  light  is 
known  to  be  only  three-fourths  of  what  it  is  in  air,  it  would 
take  one  and  one-third  times  as  long  for  the  light  to  pass 
from  the  center  of  the  objective  to  the  cross-wires,  and 
hence  we  ought  to  observe,  not  the  actual  angle  of  aberration, 
but  one  which  should  be  one-third  greater.  The  experiment 
was  actually  tried.  A  telescope  was  filled  with  water,  and 
observations  on  various  stars  were  continued  throusfhoat  the 
greater  part  of  the  year,  with  the  result  that  almost  exactly 
the  same  value  was  found  for  the  angle  of  aberration. 

This  result  was  considered  a  very  serious  objection  to  the 
undulatory  theory  until  an  explanation  was  found  by  Fresnel. 
He  proposed  that  we  consider  that  the  medium  which  trans- 
mits the  light  vibrations  is  carried  along  by  the  motion  of  the 
water  in  the  telescope  in  the  direction  of  the  motion  of  the 


152  Light  Waves  and  Their  Uses 

earth  around  the  sun.  Now,  if  the  light  waves  were  carried 
along  with  the  fnll  velocity  of  the  earth  in  its  orbit,  we  should 
be  in  the  same  difficulty,  or  in  a  more  serious  difficulty,  than 
before.  Fresnel,  however,  made  the  further  supposition  that 
the  velocity  of  the  carrying  along  of  the  light  waves  by  the 
motion  of  the  medium  was  less  than  the  actual  velocity  of  the 
medium  itself,  by  a  quantity  which  depended  on  the  index  of 
refraction  of  the  substance.  In  the  case  of  water  the  value 
of  this  factor  is  seven-sixteenths. 

This,  at  first  sight,  seems  a  rather  forced  explanation  ; 
indeed,  at  the  time  it  was  proposed  it  was  treated  with  con- 
siderable incredulity.  An  experiment  was  made  by  Fizeau, 
however,  to  test  the  point  —  in  my  opinion  one  of  the  most 
ingenious  experiments  that  have  ever  been  attempted  in 
the  whole  domain  of  physics.  The  problem  is  to  find 
the  increase  in  the  velocity  of  light  due  to  a  motion  of  the 
medium.  We  have  an  analogous  problem  in  the  case  of 
sound,  but  in  this  case  it  is  a  very  much  simpler  matter.  We 
know  by  actual  experiment,  as  we  should  infer  without  experi- 
ment, that  the  velocity  of  sound  is  increased  by  the  velocity 
of  a  wind  which  carries  the  air  in  the  same  direction,  or 
diminished  if  the  wind  moves  in  the  opposite  direction.  But 
in  the  case  of  light  waves  the  velocity  is  so  enormously 
great  that  it  would  seem,  at  first  sight,  altogether  out  of  the 
question  to  compare  it  with  any  velocity  which  we  might  be 
able  to  obtain  in  a  transparent  medium  such  as  water  or 
glass.  The  problem  consists  in  finding  the  change  in  the 
velocity  of  light  produced  by  the  greatest  velocity  we  can 
get  —  about  twenty  feet  a  second  —  in  a  column  of  water 
through  which  light  waves  pass.  We  thus  have  to  find 
a  difference  of  the  order  of  twenty  feet  in  186,000  miles, 
i.  e.,  of  one  part  in  50,000,000.  Besides,  we  can  get  only 
a  relatively  small  column  of  water  to  pass  light  through  and 
still  see  the  lijjht  when  it  returns. 


The  Ethek  153 


The  difficulty  is  met,  however,  by  taking  advantage  of 
the  excessive  minuteness  of  light  waves  themselves.  This 
double  length  of  the  water  column  is  something  like  forty 
feet.  In  this  forty  feet  there  are,  in  round  numbers, 
14,000,000  waves.  Hence  the  difference  due  to  a  velocity 
of  twenty  feet  per  second,  which  is  the  velocity  of  the  water 
current,  would  produce  a  displacement  of  the  interference 
fringes  (produced  by  two  beams,  one  of  which  passes  down 
the  column  and  the  other  up  the  column  of  the  moving 
liquid)  of  about  one-half  a  fringe,  which  corresponds  to 
a  difference  of  one-half  a  light  wave  in  the  paths.  Revers- 
ing the  water  current  should  produce  a  shifting  of  one-half 
a  fringe  in  the  opposite  direction,  so  that  the  total  shifting 
would  actually  be  of  the  order  of  one  interference  fringe. 
But  we  can  easily  observe  one -tenth  of  a  fringe,  or  in  some 
cases  even  less  than  that.  Now,  one  fringe  would  be  the 
displacement  if  water  is  the  medium  which  transmits  the 
light  waves.  But  this  other  medium  we  have  been  talking 
about  moves,  according  to  Fresnel,  with  a  smaller  velocity 
than  the  water,  and  the  ratio  of  the  velocity  of  the  medium 
to  the  velocity  of  the  water  should  be  a  particular  fraction, 
namely,  seven-sixteenths.  In  other  words,  then,  instead  of 
the  whole  fringe  we  ought  to  get  a  displacement  of  seven- 
sixteenths  of  a  fringe  by  the  reversal  of  the  water  current. 
The  experiment  was  actually  tried  by  Fizeau,  and  the  result 
was  that  the  fringes  were  shifted  by  a  quantity  less  than 
they  should  have  been  if  water  had  been  the  medium;  and 
hence  we  conclude  that  the  water  was  not  the  medium  which 
carried  the  vibrations. 

The  arrangement  of  the  apparatus  which  was  used  in  the 
experiment  is  shown  in  Fig.  105.  The  light  starts  from  a 
narrow  slit  S,  is  rendered  parallel  by  a  lens  L,  and  separated 
into  two  pencils  by  apertures  in  front  of  the  two  tubes  TT, 
which  carry  the  column  of  water.      Both  tubes  are  closed  by 


154 


Light  Waves  and  Their  Uses 


pieces  of  the  same  plane-parallel  plate  of  glass.  The  light 
passes  through  these  two  tubes  and  is  brought  to  a  focus  by 
the  lens  in  condition  to  produce  interference  fringes.  The 
apparatus  might  have  been  arranged  in  this  way  but  for 
the  fact  that  there  would  be  changes  in  the  position  of  the 
interference  fringes  whenever  the  density  or  temperature 
of  the  medium  changed;  and,  in  particular,  whenever  the 
current  changes  direction  there  would  be  produced  altera- 
tions in  length  and  changes  in  density ;  and  these  exceedingly 


FIG.  105 


slight  differences  are  quite  sufficient  to  account  for  any  motion 
of  the  fringes.  In  order  to  avoid  this  disturbance,  Fresnel  had 
the  idea  of  placing  at  the  focus  of  the  lens  the  mirror  3f,  so  that 
the  two  rays  return,  the  one  which  came  through  the  upper 
tube  going  back  through  the  lower,  and  vice  versa  for  the 
other  ray.  In  this  way  the  two  rays  pass  through  identical 
paths  and  come  together  at  the  same  point  from  which  they 
started.  With  this  arrangement,  if  there  is  any  shifting  of 
the  fringes,  it  must  be  due  to  the  reversal  of  the  change 
in  velocity  due  to  the  current  of  water.  For  one  of  the 
two  beams,  say  the  upper  one,  travels  with  the  current 
in  both  tubes;  the  other,  starting  at  the  same  point,  travels 
against  the  current  in  both  tubes.  Upon  reversing  the 
direction  of  the  current  of  water  the  circumstances  are 
exactly  the  reverse:  the  beam  which  before  traveled  with 
the  current  now  travels  against  it,  etc.  The  result  of  the 
experiment,  as  before  stated,  was  that  there  was  produced  a 


The  Ether 


155 


displacement  of  less  than  should  have  been  produced  by  the 
motion  of  the  liquid.  How  much  less  was  not  determined. 
To  this  extent  the  experiment  was  imperfect. 

On  this  account,  and  also  for  the  reason  that  the  experiment 
was  regarded  as  one  of  the  most  important  in  the  entire  subject 
of  optics,  it  seemed  to  me  that  it  was  desirable  to  repeat  it 


FIG.  106 


in  order  to  determine,  not  only  the  fact  that  the  displace- 
ment was  less  than  could  be  accounted  for  by  the  motion 
of  the  water,  but  also,  if  possible,  how  much  less.  For  this 
purpose  the  apparatus  was  modified  in  several  important 
points,  and  is  shown  in  Fig.  106. 

It  will  be  noted  that  the  principle  of  the  interferometer 
has  been  used  to  produce  interference  fringes  of  consider- 
able breadth  without  at  the  same  time  reducing  the  inten- 
sity of  the  light.  Otherwise,  the  experiment  is  essentially 
the  same  as  that  made  by  Fizeau.  The  light  starts  from  a 
bright  flame  of  ordinary  gas  light,  is  rendered  parallel  by 
the  lens,  and  then  falls  on  the  surface,  which  divides  it  into 
two  parts,  one  reflected  and  one  transmitted.     The  reflected 


156  Light  Waves  and  Theik  Uses 

portion  goes  down  one  tube,  is  reflected  twice  by  the  total 
reflection  prism  P  through  the  other  tube,  and  passes,  after 
necessary  reflection,  into  the  observing  telescope.  The  other 
ray  pursues  the  contrary  path,  and  we  see  interference  fringes 
in  the  telescope  as  before,  but  enormously  brighter  and  more 
definite.  This  arrangement  made  it  possible  to  make  meas- 
urements of  the  displacement  of  the  fringes  which  were  very 
accurate.  The  result  of  the  experiment  was  that  the  meas- 
ured displacement  was  almost  exactly  seven-sixteenths  of 
what  it  would  have  been  had  the  medium  which  transmits 
the  light  waves  moved  with  the  velocity  of  the  water. 

It  was  at  one  time  proposed  to  test  this  problem  by  utiliz- 
ing the  velocity  of  the  earth  in  its  orbit.  Since  this  velocity 
is  so  very  much  greater  than  anything  we  can  produce  at 
the  earth's  surface,  it  was  supposed  that  such  measurements 
could  be  made  with  considerable  ease ;  and  they  were  actually 
tried  in  quite  a  considerable  number  of  different  ways  and 
by  very  eminent  men.  The  fact  is,  we  cannot  utilize  the 
velocity  of  the  earth  in  its  orbit  for  such  experiments,  for 
the  reason  that  we  have  to  determine  our  directions  by  points 
outside  of  the  earth,  and  the  only  thing  we  have  is  the  stars, 
and  the  stars  are  displaced  by  this  very  element  which  we 
want  to  measure;  so  the  results  would  be  entirely  negative. 
It  was  pointed  out  by  Lorentz  that  it  is  impossible  by  any 
measurements  made  on  the  surface  of  the  earth  to  detect  any 
effect  of  the  earth's  motion. 

Maxwell  considered  it  possible,  theoretically  at  least, 
to  deal  with  the  square  of  the  ratio  of  the  two  velocities; 
that  is,  the  square  of  yom'  o^  touo-d-oito-o--  He  further 
indicated  that  if  we  made  two  measurements  of  the  velocity 
of  light,  one  in  the  direction  in  which  the  earth*  is  travel 
ing  in  its  orbit,  and  one  in  a  direction  at  right  angles  to 
this,  then  the  time  it  takes  light  to  pass  over  the  same 


The  Ethek  157 


length  of  path  is  greater  in  the  first  case  than  in  the 
second. 

We  can  easily  appreciate  the  fact  that  the  time  is  greater 
in  this  case,  by  considering  a  man  rowing  in  a  boat,  first  in  a 
smooth  pond  and  then  in  a  river.  If  he  rows  at  the  rate  of 
four  miles  an  hour,  for  example,  and  the  distance  between 
the  stations  is  twelve  miles,  then  it  would  take  him  three 
hours  to  pull  there  and  three  to  pull  back  —  six  hours  in 
all.  This  is  his  time  when  there  is  no  current.  If  there 
is  a  current,  suppose  at  the  rate  of  one  mile  an  hour, 
then  the  time  it  would  take  to  go  from  one  point  to 
the  other,  would  be,  not  12  divided  by  4,  but  12  divided  by 
4  +  1,  i.  e.,  2.4  hours.  In  coming  back  the  time  would  be 
12  divided  by  4  —  1,  which  would  be  4  hours,  and  this 
added  to  the  other  time  equals  6.4  instead  of  6  hours.  It 
takes  him  longer,  then,  to  pass  back  and  forth  when  the 
medium  is  in  motion  than  when  the  medium  is  at  rest. 
We  can  understand,  then,  that  it  would  take  light  longer  to 
travel  back  and  forth  in  the  direction  of  the  motion  of  the 
earth.  The  difference  in  the  times  is,  however,  so  exceedingly 
small,  being  of  the  order  of  1  in  100,000,000,  that  Maxwell 
considered  it  practically  hopeless  to  attempt  to  detect  it. 

In  spite  of  this  apparently  hopeless  smallness  of  the 
quantities  to  be  observed,  it  was  thought  that  the  minute- 
ness of  the  light  waves  might  again  come  to  our  rescue. 
As  a  matter  of  fact,  an  experiment  was  devised  for  detect- 
ing this  small  quantity.  The  conditions  which  the  appa- 
ratus must  fulfil  are  rather  complex.  The  total  distance 
traveled  must  be  as  great  as  possible,  something  of  the  order 
of  one  hundred  million  waves,  for  example.  Another  condi- 
tion requires  that  we  be  able  to  interchange  the  direction 
without  altering  the  adjustment  by  even  the  one  hundredth- 
millionth  part.  Further,  the  apparatus  must  be  absolutely 
free  from  vibration. 


158  Light  Waves  and  Their  Uses 

The  problem  was  practically  solved  by  reflecting  part  of 
the  light  back  and  forth  a  number  of  times  and  then  returning 
it  to  its  starting-point.  The  other  path  was  at  right  angles  to 
the  first,  and  over  it  the  light  made  a  similar  series  of  excur- 
sions, and  was  also  reflected  back  to  the  starting-point.  This 
starting-point  was  a  separating  plane  in  an  interferometer, 
and  the  two  paths  at  right  angles  were  the  two  arms  of  an 
interferometer.  Notwithstanding  the  very  considerable  dif- 
ference in  path,  which  must  involve  an  exceedingly  high  order 
of  accuracy  in  the  reflecting  surfaces  and  a  constancy  of 
temperature  in  the  air  between,  it  was  possible  to  see  fringes 
and  to  keep  them  in  position  for  several  hours  at  a  time. 

These  conditions  having  been  fulfilled,  the  apparatus  was 
mounted  on  a  stone  support,  about  four  feet  square  and  one 
foot  thick,  and  this  stone  was  mounted  on  a  circular  disc  of 
wood  which  floated  in  a  tank  of  mercury.  The  resistance  to 
motion  is  thus  exceedingly  small,  so  that  by  a  very  slight 
pressure  on  the  circumference  the  whole  could  be  kept  in  slow 
and  continuous  rotation.  It  would  take,  perhaps,  five  minutes 
to  make  one  single  turn.  With  this  slight  motion  there 
is  practically  no  oscillation;  the  observer  has  to  follow 
around  and  at  intervals  to  observe  whether  there  is  any 
displacement  of  the  fringes. 

It  was  found  that  there  was  no  displacement  of  the 
interference  fringes,  so  that  the  result  of  the  experiment 
was  negative  and  would,  therefore,  show  that  there  is  still 
a  difficulty  in  the  theory  itself;  and  this  difficulty,  I  may 
say,  has  not  yet  been  satisfactorily  explained.  I  am  present- 
ing the  case,  not  so  much  for  solution,  but  as  an  illustration 
of  the  applicability  of  light  waves  to  new  problems. 

The  actual  arrangement  of  the  experiment  is  shown  in 
Fig.  107.  A  lens  makes  the  rays  nearly  parallel.  The 
dividing  surface  and  the  two  paths  are  easily  recognized.  The 
telescope  was  furnished  with  a  micrometer  screw  to  determine 


The  Ethek 


159 


^X 


//. 


\*  /yd 


U7/y 


the  amount  of  displacement  of  the  fringes,  if  there  were  any. 
The  last  mirror  is  mounted  on  a  slide;  so  these  two  paths 
may  be  made  equal  to  the  necessary  degree  of  accuracy — 
something  of  the  order  of  one  fifty-thousandth  of  an  inch. 

Fig.  108  represents  the  actual  apparatus.  The  stone  and 
the  circular  disc  of  wood  sup- 
porting the  stone  in  the  tank 
filled  with  mercury  are  readily 
recognized;  also  the  dividing 
surface  and  the  various  mirrors. 

It  was  considered  that,  if 
this  experiment  gave  a  posi- 
tive result,  it  would  determine 
the  velocity,  not  merely  of  the 
earth  in  its  orbit,  but  of  the 
earth  through  the  ether.  With 
good  reason  it  is  supposed  that 
the  sun  and  all  the  planets  as 
well  are  moving  through  space  at  a  rate  of  perhaps  twenty 
miles  per  second  in  a  certain  particular  direction.  The  velocity 
is  not  very  well  determined,  and  it  was  hoped  that  with  this 
experiment  we  could  measure  this  velocity  of  the  whole  solar 
system  through  space.  Since  the  result  of  the  experiment 
was  negative,  this  problem  is  still  demanding  a  solution. 

The  experiment  is  to  me  historically  interesting,  because 
it  was  for  the  solution  of  this  problem  that  the  interferometer 
was  devised.  I  think  it  will  be  admitted  that  the  problem, 
by  leading  to  the  invention  of  the  interferometer,  more  than 
compensated  for  the  fact  that  this  particular  experiment  gave 
a  negative  result. 


X 


FIG.  107 


From  all  that  precedes  it  appears  practically  certain  that 
there  must  be  a  medium  whose  proper  function  it  is  to  trans- 
mit light  waves.     Such  a  medium  is  also  necessary  for  the 


160 


Light  Waves  and  Thbie  Uses 


transmission  of  electrical  and  magnetic  effects.  Indeed,  it 
is  fairly  well  established  that  light  is  an  electro-magnetic 
disturbance,  like  that  due  to  a  discharge  from  an  induction  coil 
or  a  condenser.  Such  electric  waves  can  be  reflected  and 
refracted  and  polarized,  and  be  made  to  produce  vibrations 


FIG.  108 


and  other  changes,  just  as  the  light  waves  can.  The  only 
difference  between  them  and  the  light  waves  is  in  the  wave 
length. 

This  difference  may  be  enormous  or  quite  moderate.  For 
example,  a  telegraphic  wave,  which  is  practically  an  electro- 
magnetic disturbance,  may  be  as  long  as  one  thousand  miles. 
The  waves  produced  by  the  oscillations  of  a  condenser,  like 
a  Leyden  jar,  may  be  as  short  as  one  hundred  feet ;  the  waves 
produced  by  a  Hertz  oscillator  may  be  as  short  as  one-tenth 
of  an  inch.  Between  this  and  the  longest  light  wave  there 
is  not  an  enormous  gap,  for  the  latter  has  a  length  of  about 
one-thousandth  of  an  inch.     Thus  the  difference  between  the 


The  Ether  161 


Hertz  vibrations  and  the  longest  light  wave  is  less  than  the 
difference  between  the  longest  and  shortest  light  waves,  for 
some  of  the  shortest  oscillations  are  only  a  few  millionths  of 
an  inch  long.  Doubtless  even  this  gap  will  soon  be  bridged 
over. 

The  settlement  of  the  fact  that  light  is  a  magneto-elec- 
tric oscillation  is  in  no  sense  an  explanation  of  the  nature 
of  light.  It  is  only  a  transference  of  the  problem,  for  the 
question  then  arises  as  to  the  nature  of  the  medium  and  of 
the  mechanical  actions  involved  in  such  a  medium  which 
sustains  and  transmits  these  electro-magnetic  disturbances. 

A  suggestion  which  is  very  attractive  on  account  of  its 
simplicity  is  that  the  ether  itself  is  electricity ;  a  much  more 
probable  one  is  that  electricity  is  an  ether  strain — -that  a 
displacement  of  the  ether  is  equivalent  to  an  electric  current. 
If  this  is  true,  we  are  returning  to  our  elastic-solid  theory. 
I  may  quote  a  statement  which  Lord  Kelvin  made  in  reply 
to  a  rather  skeptical  question  as  to  the  existence  of  a  me- 
dium about  which  so  very  little  is  supposed  to  be  known. 
The  reply  was:  "Yes,  ether  is  the  only  form  of  matter  about 
which  we  know  anything  at  all."  In  fact,  the  moment  we 
begin  to  inquire  into  the  nature  of  the  ultimate  particles  of 
ordinary  matter,  we  are  at  once  enveloped  in  a  sea  of  con- 
jecture and  hypotheses — all  of  great  difficulty  and  complexity. 

One  of  the  most  promising  of  these  hypotheses  is  the 
"ether  vortex  theory,"  which,  if  true,  has  the  merit  of  intro- 
ducing nothing  new  into  the  hypotheses  already  made,  but 
only  of  specifying  the  particular  form  of  motion  required. 
The  most  natural  form  of  such  vortex  motions  with  which 
to  deal  is  that  illustrated  by  ordinary  smoke  rings,  such  as 
are  frequently  blown  from  the  stack  of  a  locomotive.  Such 
vortex  rings  may  easily  be  produced  by  filling  with  smoke 
a  box  which  has  a  circular  aperture  at  one  end  and  a  rubber 
diaphragm  at  the  other,  and  then  tapping  the  rubber.      The 


162  Light  Waves  and  Theik  Uses 

friction  against  the  side  of  the  opening,  as  the  pufp  of  smoke 
passes  out,  produces  a  rotary  motion,  and  the  result  will  be 
smoke  rings  or  vortices. 

Investigation  shows  that  these  smoke  rings  possess,  to  a 
certain  degree,  the  properties  which  we  are  accustomed  to 
associate  with  atoms,  notwithstanding  the  fact  that  the 
medium  in  which  these  smoke  rings  exists  is  far  from  ideal. 
If  the  medium  were  ideal,  it  would  be  devoid  of  friction, 
and  then  the  motion,  when  once  started,  would  continue 
indefinitely,  and  that  part  of  the  ether  which  is  differentiated 
by  this,  motion  would  ever  remain  so. 

Another  peculiarity  of  the  ring  is  that  it  cannot  be  cut 
— it  simply  winds  around  the  knife.  Of  course,  in  a  very 
short  time  the  motion  in  a  smoke  ring  ceases  in  consequence 
of  the  viscosity  of  the  air,  but  it  would  continue  indefinitely 
in  such  a  frictionless  medium  as  we  suppose  the  ether  to  be. 

There  are  a  number  of  other  analogies  which  we  have 
not  time  to  enter  into^ — quite  a  number  of  details  and 
instances  of  the  interactions  of  the  various  atoms  which  have 
been  investigated.  In  fact,  there  are  so  many  analogies 
that  we  are  tempted  to  think  that  the  vortex  ring  is  in  reality 
an  enlarged  image  of  the  atom.  The  mathematics  of  the 
subject  is  unfortunately  very  difficult,  and  this  seems  to  be 
one  of  the  principal  reasons  for  the  slow  progress  made  in 
the  theory. 

Suppose  that  an  ether  strain  corresponds  to  an  electric 
charge,  an  ether  displacement  to  the  electric  current,  these 
ether  vortices  to  the  atoms — if  we  continue  these  supposi- 
tions, we  arrive  at  what  may  be  one  of  the  grandest  general- 
izations of  modern  science — of  which  we  are  tempted  to  say 
that  it  ought  to  be  true  even  if  it  is  not  —  namely,  that  all 
the  phenomena  of  the  physical  universe  are  only  different 
manifestations  of  the  various  modes  of  motions  of  one  all- 
pervading  substance  —  the  ether. 


The  Ether  103 


All  modern  investigation  tends  toward  the  elucidation  of 
this  problem,  and  the  day  seems  not  far  distant  when  the 
converging  lines  from  many  apparently  remote  regions  of 
thought  will  meet  on  this  common  ground.  Then  the 
nature  of  the  atoms,  and  the  forces  called  into  play  in  their 
chemical  union;  the  interactions  between  these  atoms  and 
the  non-differentiated  ether  as  manifested  in  the  phenomena 
of  light  and  electricity;  the  structures  of  the  molecules  and 
molecular  systems  of  which  the  atoms  are  the  units;  the 
explanation  of  cohesion,  elasticity,  and  gravitation  —  all 
these  will  be  marshaled  into  a  single  compact  and  consistent 
body  of  scientific  knowledge. 

SUMMARY 

1.  A  number  of  independent  courses  of  reasoning  lead  to 
the  conclusion  that  the  medium  which  propagates  light  waves 
is  not  an  ordinary  form  of  matter.  Little  as  we  know  about 
it,  we  may  say  that  our  ignorance  of  ordinary  matter  is  still 
greater. 

2.  In  all  probability,  it  not  only  exists  where  ordinary 
matter  does  not,  but  it  also  permeates  all  forms  of  matter. 
The  motion  of  a  medium  such  as  water  is  found  not  to  add 
its  full  value  to  :the  velocity  of  light  moving  through  it,  but 
only  such  a  fraction  of  it  as  is  perhaps  accounted  for  on  the 
hypothesis  that  the  ether  itself  does  not  partake  of  this  motion. 

3.  The  phenomenon  of  the  aberration  of  the  fixed  stars 
can  be  accounted  for  on  the  hypothesis  that  the  ether  does 
not  partake  of  the  earth's  motion  in  its  revolution  about 
the  sun.  All  experiments  for  testing  this  hypothesis  have, 
however,  given  negative  results,  so  that  the  theory  may  still 
be  said  to  be  in  an  unsatisfactory  condition. 


INDEX. 


Aberration,  149. 

Accuracy  of  measurement:  value  of 
increasing,  23;  limit  without  lenses, 
25 ;  limit  with  lenses,  27  ;  increase  due 
to  lenses,  30;  increase  due  to  interfer- 
ometer, 36 ;  of  standards  of  length  with 
grating,  85 ;  of  length  of  seconds  pen- 
dulum, 86 ;  of  earth's  circumference,  87  ; 
of  wave  length- with  the  interferometer, 
98. 

Air  wedge  :  interference  produced  by, 
15. 

Amphipleura  pellucida  :  use  as  test  of 
resolution,  30. 

Amplitude,  6. 

Analysis:  of  periodic  curves,  68;  of  the 
nature  of  a  source  of  light,  76. 

Analyzer  :  harmonic,  68. 

Arago  :  velocity  of  light,  48 ;  interfer- 
ometer, 51. 

Beats  :  between  tuning-forks,  12. 

Black  spot  :  on  soap  film,  53 ;  thickness 
of,  54. 

Boiling  of  star  images,  129. 

Bradley  :  aberration,  149. 

BuRNHAM:  Jupiter's  satellites,  142. 

Cadmium  :  analysis  of  radiations  of,  81 ; 
red  radiation  as  standard  of  length, 
91 ;  number  of  waves  in  meter,  98 ;  ac- 
tion of  magnetism  on  radiations  of, 
116. 

Comets  :  resistance  by  ether  to  motion 
of,  45. 

Corpuscular  theory,  44. 

Diffraction:  of  sound  waves,  19;  in 
telescope  and  microscope,  29 ;  by  rec- 
tangular opening,  32. 

Diffraction  pattern  :  due  to  circular 
opening,  29,  1.30;  due  to  rectangular 
opening,  133;  due  to  two  slits,  134. 

Double  slit  :  use  of  in  astronomical 
work,  134. 

Earth:  resistance  by  ether  to  motion 
of,  45,  148 ;  circumference  of  as  stand- 
ard of  length,  87. 

Echelon  spectroscope,  122. 

Efficiency:    of   microscope    and  tele- 
scope, 25. 
Electrolysis,  113. 

Electromagnetic  nature  of  light, 
160. 

Engelmann  :  Jupiter's  satellites,  142. 
Ether:   properties  of,  45,  146;   vortex- 
theory  of,  161. 


Expansion  :  measurement  of  coefficient 

of,  55. 
Faraday  :  action  of  magnetism  on  light, 

107. 

Fievez:  action  of  magnetism  on  light, 
107. 

Fitzgerald  :  action  of  magnetism  on 
light,  112. 

FiZEAU :  velocity  of  light,  48 ;  in  mov- 
ing media,  152. 

FoucAULT :  velocity  of  light,  48. 

Fraunhofer  :  lines  in  solar  spectrum, 
60. 

Fresnel  :  measurement  of  index  of  re- 
fraction, 51 ;  moving  media,  152. 

Fringes  :  due  to  two  openings,  .33 ; 
breadth  of,  34 ;  use  of  in  spectrum  anal- 
ysis, 64. 

Gases  :  liquefaction  of,  24. 

Gould  :  standards  of  length,  84,  103. 

Grating  :  diffraction,  23,  84,  119 ;  effici- 
ency of,  121. 

Gravitation  constant  :  measurement 
with  interferometer,  56. 

Gun  sight  :  use  in  measuring  angles,  25. 

Harmonic  motion,  6 ;  analyzer,  68. 

Hertz  :  oscillator,  160. 

Hough:  Jupiter's  satellites,  142. 

Hydrogen  :  analysis  of  radiations  of,  78. 

Image:  formation  of,  26. 

Interference  :  definition  of,  8 ;  of  sound 
waves,  9 ;  of  mercury  ripples,  11 ;  of 
light  in  soap  film,  12;  of  two  trains  of 
waves,  64. 

Interferometer:  definition  of,  33,  36; 
description  of,  40;  application  of  to 
measure  index  of  refraction,  51 ;  to 
measure  thickness  of  soap  film,  53;  to 
measure  coefficient  of  expansion,  55 ; 
to  measure  gravitation  constant,  56; 
to  test  screws,  57 ;  to  measure  light 
waves,  58;  to  analyze  spectral  lines, 
60,  73,  78;  to  determine  standards  of 
length,  89;  to  theZeeman  effect,  108, 
114;  to  astronomical  measurements, 
127 ;  to  aberration,  157. 

Intermediate  standards  of  length. 
93. 

Iron  :  spectrum  of,  62.  ' 

Johonnott  :  thickness  of  liquid  films, 
54. 

Jupiter,  128;  size  of  satellites,  141. 
Kelvin  :   dynamic  model  of  wave  mo- 
tion, 5,  16. 


165 


166 


Index 


Laemoe  :  action  of  magnetism  on  light, 
112. 

Lens  :  formation  of  image  by,  26. 

Leyekeiee  :  discovery  of  Uranus,  24. 

LixEAE  MEASUEEMENTS  :  attainable  ac- 
curacy in,  25. 

LoEENTZ :  action  of  magnetism  on  light, 
112 ;  aberration,  156. 

Magnetism  :  action  on  light,  107. 

Magnification  :  produced  by  lens,  27  ; 
loss  of  light  in,  27  ;  of  fringes  by  inter- 
ferometer, 32. 

Manometkic  capsule,  10. 

Maes,  128. 

Maxwell  :  aberration,  156. 

Meeguey  :  analysis  of  radiations  of,  80. 

Metee:  manufacture  of,  87;  value  in 
waves  of  cadmium  light,  104. 

MiCEOSCOPE :  efficiency  of,  25 ;  limit  of 
resolution  of,  30. 

Molecules  :  complexity  of,  shown  by 
spectrum,  82. 

MoELEY :  measurement  of  coefficient  of 
expansion,  55. 

Moving  media  :  effect  on  velocity  of 
light,  151. 

Music  :  color,  2. 

Newton  :  corpuscular  theory,  45  ;  spec- 
trum, 60. 

Objective:  relation  to  size  of  dififrac- 
tion  pattern,  30. 

Pendulum:  motion  of,  6;  as  standard  of 
length,  86. 

Peeiod,  6. 

Phase  :  defined,  7 ;  loss  of  by  reflec- 
tion, 16. 

Poisson:  diffraction,  21. 

POLAEIZATION,  110. 

Quincke  :  interference  of  sound,  9. 

Rayleigh:  diffraction  of  sound,  21 ;  dis- 
covery of  Argon,  24. 

Eeflection  :  change  of  phase  on,  16. 

Refraction  :  comparison  of  theories  of, 
47 ;  index  of,  50 ;  measurement  of  in- 
dex of,  51. 

Resolution:  of  telescope,  29,130;  of  mi- 
croscope, 30;  of  spectroscope,  62;  of 
grating,  121 ;  of  echelon,  125. 

Revolving  mieeoe,  48. 

Ripples  :  interference  of  on  surface  of 
mercury,  11. 


Rogers:  measurement  of  coefficient  of 
expansion,  55. 

RUSKIN.I. 

Satuen,  12«. 

Screw  :  testing  with  interferometer,  57. 

Sensitive  flame,  19. 

Simple  harmonic  motion,  6 ;  curve,  7. 

Sine  curve,  7. 

Slit  :  diffraction  produced  by,  22. 

Soap  film  :  colors  of,  14. 

Sodium:  spectrum  of,  61:  distance  be- 
tween lines  a  standard  of  measure- 
ment, 62 ;  distance  between  lines  of, 
66;  analysis  of  radiatioris  of ,  78 ;  action 
of  magnetism  on  radiations  of,  107. 

Sound  waves  :  interference  of,  9 ;  dif- 
fraction of,  19 ;  shadow  produced  by, 
20. 

Source  of  light  :  distribution  of,  75. 

Spectral  lines  :  structure  of,  62 ;  analy- 
sis of  with  interferometer,  73. 

Spectrum,  60;  of  sodium,  61,  78;  of  hy- 
drogen, 78;  of  thallium,  79;  of  mer- 
cury, 80 ;  of  cadmium,  81 ;  order  of,  121. 

Standards  of  length,  86. 

Star  discs  :  size  of,  143. 

Steuve  :  Jupiter's  satellites,  142. 

Telescope:  efficiency  of,  25;  limit  of 
resolution  of,  29, 130. 

Thallium  :  analysis  of  radiations  of,  79. 

Tuning-foeks  :  beats  formed  by,  12. 

Undulatoey  theory,  44. 

Uranus  :  discovery  of,  24. 

Vacuum  tubes  :  as  sources  of  light,  75. 

Velocity  :  of  wave  motion,  8,  146 ;  of 
light,  146. 

Visibility  :  defined,  68 ;  curves  with  the 
interferometer,  70;  with  the  double 
slit,  139. 

Vortex  theory,  161. 

Wave  length  :  definition  of,  7 ;  meas- 
urement of,  17 ;  as  standard  of  length, 
84. 

Wave  motion,  3;  kinetic  model  of,  4; 
Kelvin's  dynamic  model  of,  5 ;  propa- 
gation of,  7. 

Wheatstone  :  velocity  of  light,  48. 

Young  :  interference,  22. 

Zeeman  :  action  of  magnetism  on  light 
107. 

Zinc  ;  spectrum  of,  62. 


PLATE  II 


PLATE  III 
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